An experiment was effectively accomplished utilizing a virtual lab. As for the calculation part, the pipe diameters of 25mm and 15mm which were tested are compared. As it is noticed, as the velocity of the fluid flow increases, the head loss increases. Besides, the friction factor increases as the pipe diameter increases. In conclusion, using velocity which has related to flow rate to compare the relationship with friction factor, which when the flow rate increase, the velocity of the fluid increase, the friction factor is decreased.
Next, the friction factor remained within 0. 001 to 0. 011 in all three trials whereas the average was 0.01. Furthermore, as it comes to head loss the pipe had 3 different readings which were between 119.7 to 81.9 cm. End of the experiment, it's proven that Reynold number, Re is more than 4000 and friction factor esteem gives an implying that the stream is hydraulically smooth.
LAND DRAINAGE- CLASSIFICATIONS, STEADY AND UNSTEADY STATE EQUATIONSNamitha M R
The document discusses classifications and equations related to land drainage. It begins by classifying drains according to their construction as either natural or artificial, and according to their function as open, closed/sub-surface, or vertical. Open drains are further divided into surface, seepage, and surface-cum-seepage drains. Closed drains include tile drains, which use pipes, and mole drains, which form channels using a mole plough. The document then presents the steady state Hooghout and Earnst equations for calculating drain spacing and head. Finally, it introduces the unsteady state Glover-Dumn equation for describing falling water tables after recharge.
The document defines and discusses several terms related to hydrology:
1. Potamology is the study of rivers, which examines rivers from five perspectives including the physics of running water and rivers as habitats for organic life.
2. Limnology is the study of biological, chemical, and physical features of lakes and other bodies of fresh water.
3. Cryology is the scientific study of ice, including areas like snow and ice mapping and classification.
This document describes an experiment conducted to demonstrate and measure fluid flow rates using different flow meter types. The experiment utilized a hydraulic bench unit with a volumetric measuring tank and submersible pump. Three common flow meters were tested: a rotameter, venture meter, and orifice plate. Readings were taken from each meter and calculations were performed to determine flow rates and discharge coefficients. Plots were made comparing actual flow rates to measured rates from each meter. The results showed the relationships between variables and effectiveness of different flow meter designs.
Head losses
Major Losses
Minor Losses
Definition • Dimensional Analysis • Types • Darcy Weisbech Equation • Major Losses • Minor Losses • Causes Head Losses
3. • Head loss is loss of energy per unit weight. • Head = Energy of Fluid / Weight • Head losses can be – Kinetic Head – Potential Head – Pressure Head 6/10/2015 4Danial Gondal Head Loss
4. • Kinetic Head – K.H. = kinetic energy / Weight = v² /2g • Potential Head – P.H = Potential Energy / Weight = mgz /mg = z • Pressure Head – P.H = P/ ρ g 6/10/2015 5
5. • (P/ ρ g) + (v² /2g ) + (z) = constant • (FL-2F-1L3LT-2L-1T2) + (L2T-2L1T2)+(L) = constant • (L) + (L) + (L) = constant • As L represent height so it is dimensionally L. 6/10/2015 6 Dimensional Analysis
6. • However the equation (P/ ρ g) + (v² /2g ) + (z) = constant Is valid for Bernoulli's Inviscid flow case. As we are studying viscous flow so (P1/ ρ g) + (v1² /2g ) + (z1) = EGL1(Energy Grade Line At point 1) (P2/ ρ g) + (v2² /2g ) + (z2) = EGL2(Energy Grade Line At point 2) 6/10/2015 7 Head Loss
7. • For Inviscid Flow EGL1 - EGL2= 0 • For Viscous Flow EGL1 - EGL2= Hf 6/10/2015 8 Head Loss
8. MAJOR LOSSES IN PIPES
9. •Friction loss is the loss of energy or “head” that occurs in pipe flow due to viscous effects generated by the surface of the pipe. • Friction Loss is considered as a "major loss" •In mechanical systems such as internal combustion engines, it refers to the power lost overcoming the friction between two moving surfaces. •This energy drop is dependent on the wall shear stress (τ) between the fluid and pipe surface. 6/10/2015 10 Friction Loss
10. •The shear stress of a flow is also dependent on whether the flow is turbulent or laminar. •For turbulent flow, the pressure drop is dependent on the roughness of the surface. •In laminar flow, the roughness effects of the wall are negligible because, in turbulent flow, a thin viscous layer is formed near the pipe surface that causes a loss in energy, while in laminar flow, this viscous layer is non-existent. 6/10/2015 11 Friction Loss
11. Frictional head losses are losses due to shear stress on the pipe walls. The general equation for head loss due to friction is the Darcy-Weisbach equation, which is where f = Darcy-Weisbach friction factor, L = length of pipe, D = pipe diameter, and V = cross sectional average flow velocity.
Precipitation is the natural process of conversion of atmospheric water vapour into water. The water falls(comes down) in the form of a rainfall or snow fall. The term precipitation is also used to refer rainfall. It is term and includes all forms of falling moisture viz., rainfall, snowfall, sleet, hail etc. Rainfall occurs in the form of a pattern.
Precipitation occurs when moisture from the atmosphere reaches the Earth's surface. There are several types of precipitation including rain, snow, hail, fog, dew, mist, glaze, rime, and sleet. Precipitation forms through convectional, orographic, and cyclonic/frontal mechanisms. Rainfall and snowfall are most commonly measured using non-recording and recording rain gauges, which collect precipitation and allow measurement of amount, intensity, and duration. Proper siting and placement of rain gauges is important to obtain accurate precipitation measurements.
DENSITY AND SPECIFIC GRAVITY (Density determination of liquids by using hydro...Zanyar qaradaxe
This experiment measured the density and specific gravity of naphtha using a hydrometer. The hydrometer reading for naphtha was 0.695 at an actual temperature of 21°C. The specific gravity was then corrected to the standard temperature of 15.6°C, yielding a value of 0.697592. Calculations were shown to determine the density of naphtha at 15.6°C as 0.697 g/cm3. The hydrometer method was discussed as the simplest way to determine liquid density and specific gravity based on Archimedes' principle.
LAND DRAINAGE- CLASSIFICATIONS, STEADY AND UNSTEADY STATE EQUATIONSNamitha M R
The document discusses classifications and equations related to land drainage. It begins by classifying drains according to their construction as either natural or artificial, and according to their function as open, closed/sub-surface, or vertical. Open drains are further divided into surface, seepage, and surface-cum-seepage drains. Closed drains include tile drains, which use pipes, and mole drains, which form channels using a mole plough. The document then presents the steady state Hooghout and Earnst equations for calculating drain spacing and head. Finally, it introduces the unsteady state Glover-Dumn equation for describing falling water tables after recharge.
The document defines and discusses several terms related to hydrology:
1. Potamology is the study of rivers, which examines rivers from five perspectives including the physics of running water and rivers as habitats for organic life.
2. Limnology is the study of biological, chemical, and physical features of lakes and other bodies of fresh water.
3. Cryology is the scientific study of ice, including areas like snow and ice mapping and classification.
This document describes an experiment conducted to demonstrate and measure fluid flow rates using different flow meter types. The experiment utilized a hydraulic bench unit with a volumetric measuring tank and submersible pump. Three common flow meters were tested: a rotameter, venture meter, and orifice plate. Readings were taken from each meter and calculations were performed to determine flow rates and discharge coefficients. Plots were made comparing actual flow rates to measured rates from each meter. The results showed the relationships between variables and effectiveness of different flow meter designs.
Head losses
Major Losses
Minor Losses
Definition • Dimensional Analysis • Types • Darcy Weisbech Equation • Major Losses • Minor Losses • Causes Head Losses
3. • Head loss is loss of energy per unit weight. • Head = Energy of Fluid / Weight • Head losses can be – Kinetic Head – Potential Head – Pressure Head 6/10/2015 4Danial Gondal Head Loss
4. • Kinetic Head – K.H. = kinetic energy / Weight = v² /2g • Potential Head – P.H = Potential Energy / Weight = mgz /mg = z • Pressure Head – P.H = P/ ρ g 6/10/2015 5
5. • (P/ ρ g) + (v² /2g ) + (z) = constant • (FL-2F-1L3LT-2L-1T2) + (L2T-2L1T2)+(L) = constant • (L) + (L) + (L) = constant • As L represent height so it is dimensionally L. 6/10/2015 6 Dimensional Analysis
6. • However the equation (P/ ρ g) + (v² /2g ) + (z) = constant Is valid for Bernoulli's Inviscid flow case. As we are studying viscous flow so (P1/ ρ g) + (v1² /2g ) + (z1) = EGL1(Energy Grade Line At point 1) (P2/ ρ g) + (v2² /2g ) + (z2) = EGL2(Energy Grade Line At point 2) 6/10/2015 7 Head Loss
7. • For Inviscid Flow EGL1 - EGL2= 0 • For Viscous Flow EGL1 - EGL2= Hf 6/10/2015 8 Head Loss
8. MAJOR LOSSES IN PIPES
9. •Friction loss is the loss of energy or “head” that occurs in pipe flow due to viscous effects generated by the surface of the pipe. • Friction Loss is considered as a "major loss" •In mechanical systems such as internal combustion engines, it refers to the power lost overcoming the friction between two moving surfaces. •This energy drop is dependent on the wall shear stress (τ) between the fluid and pipe surface. 6/10/2015 10 Friction Loss
10. •The shear stress of a flow is also dependent on whether the flow is turbulent or laminar. •For turbulent flow, the pressure drop is dependent on the roughness of the surface. •In laminar flow, the roughness effects of the wall are negligible because, in turbulent flow, a thin viscous layer is formed near the pipe surface that causes a loss in energy, while in laminar flow, this viscous layer is non-existent. 6/10/2015 11 Friction Loss
11. Frictional head losses are losses due to shear stress on the pipe walls. The general equation for head loss due to friction is the Darcy-Weisbach equation, which is where f = Darcy-Weisbach friction factor, L = length of pipe, D = pipe diameter, and V = cross sectional average flow velocity.
Precipitation is the natural process of conversion of atmospheric water vapour into water. The water falls(comes down) in the form of a rainfall or snow fall. The term precipitation is also used to refer rainfall. It is term and includes all forms of falling moisture viz., rainfall, snowfall, sleet, hail etc. Rainfall occurs in the form of a pattern.
Precipitation occurs when moisture from the atmosphere reaches the Earth's surface. There are several types of precipitation including rain, snow, hail, fog, dew, mist, glaze, rime, and sleet. Precipitation forms through convectional, orographic, and cyclonic/frontal mechanisms. Rainfall and snowfall are most commonly measured using non-recording and recording rain gauges, which collect precipitation and allow measurement of amount, intensity, and duration. Proper siting and placement of rain gauges is important to obtain accurate precipitation measurements.
DENSITY AND SPECIFIC GRAVITY (Density determination of liquids by using hydro...Zanyar qaradaxe
This experiment measured the density and specific gravity of naphtha using a hydrometer. The hydrometer reading for naphtha was 0.695 at an actual temperature of 21°C. The specific gravity was then corrected to the standard temperature of 15.6°C, yielding a value of 0.697592. Calculations were shown to determine the density of naphtha at 15.6°C as 0.697 g/cm3. The hydrometer method was discussed as the simplest way to determine liquid density and specific gravity based on Archimedes' principle.
WATER RESOURCES ENGINEERING MODULE 1 NOTESReshmaMRaju
This document provides an overview of key concepts in hydrology and water resources engineering. It discusses the hydrologic cycle and its three main processes of evaporation, precipitation, and runoff. It describes different types of precipitation including cyclonic, convective, and orographic precipitation. Measurement of rainfall using rain gauges is also summarized, including factors to consider for the optimal number of rain gauges. Methods for estimating missing precipitation data from nearby rain gauges are outlined, such as the arithmetic mean method, normal ratio method, and inverse distance method.
The document provides design steps for a canal drop-notch structure. Key steps include:
1) Designing the trapezoidal notch including the number of notches, bottom width, and side slopes based on upstream and downstream water levels.
2) Designing the drop wall with appropriate thickness, height, and bottom width to safely convey water over the notch.
3) Designing a water cushion cistern downstream of the notch using Bligh's creep theory to determine adequate thickness to prevent uplift.
4) Designing protective works including abutments, wing walls, and revetment pitching upstream and downstream for structural integrity and erosion protection.
This document discusses local energy (head) losses that occur in pipes due to changes in pipe geometry or flow direction. It introduces minor losses that are proportional to the velocity head and defined by a loss coefficient. Specific minor losses are examined for abrupt enlargements and contractions using the continuity, momentum, and Bernoulli equations. Loss coefficients are determined experimentally and provided in tables based on the area ratio. The total head loss in a pipe system is calculated considering losses at the pipe entrance/exit and along the length. Local losses are generally negligible for long pipes.
This chapter discusses energy losses that occur in pipe networks due to fluid flow. It describes major losses, which are primarily due to friction within the pipe, and minor losses, which are secondary losses caused by changes in pipe diameter, bends, valves, and other components. Methods are provided to calculate the head loss associated with major and minor losses using equations that consider factors like pipe roughness, diameter, flow rate, and geometry of components. Worked examples are also included to demonstrate calculating head losses in pipe networks with pipes arranged in series and parallel configurations.
This document provides an introduction to hydrology, including:
1. Hydrology is defined as the science of water, its occurrence and circulation on Earth. It deals with water resources, processes like precipitation and runoff, and problems like floods and droughts.
2. The hydrologic cycle describes the continuous movement of water on, above, and below the Earth's surface, including evaporation, transpiration, precipitation, runoff, and storage components.
3. The water budget equation expresses the relationship between inputs, outputs, and changes in storage of water in a given catchment area over a period of time.
1. The document describes an experiment conducted to determine hydrostatic pressure and the center of pressure acting on a plane surface using a hydrostatic pressure apparatus.
2. The experiment involved setting the apparatus at an angle, balancing it by adding weights, and measuring the water level as more weights were added.
3. Calculations were done to find theoretical and practical hydrostatic pressures using equations for the area, height, resultant force, and center of pressure. The results showed some difference between theoretical and practical pressures.
This document describes an experiment to verify the momentum equation through measuring the impact of a water jet. The objective is to experimentally test Newton's second law of motion as it applies to fluid momentum. The apparatus required includes an impact of jet setup, weights, and a stopwatch. The theoretical basis is explained, noting that the sum of external forces equals the rate of change of momentum. The experimental setup and procedure are outlined, involving measuring the discharge and velocity of the jet using a collecting tank and nozzle, and determining the force on a target plate by adding weights to return it to its initial position. Observations are recorded for different flow rates.
The document discusses concepts related to fluid flow including continuity equations, conservation of mass, Bernoulli's equation, and venturi meters. It provides examples of calculating volume flow rate, fluid velocity, mass flow rate, and pressure given pipe dimensions and fluid properties. It also discusses how venturi meters can be used to measure flow rates based on pressure changes through the converging and diverging sections.
this is the experiment of fluid mechanics .FLOW OVER A SHARP CRESTED WEIR.experiment of weir.from this experiment we can learn discharge over the sharp crested weir and etc.
This document contains 43 questions related to hydrology and water resources engineering. The questions cover topics like the hydrologic cycle, precipitation, rainfall measurement, runoff analysis, unit hydrographs, flood frequency analysis and flood routing. Most of the questions ask students to explain hydrologic concepts, factors affecting runoff and infiltration, methods to derive unit hydrographs and questions related to flood estimation. A few questions ask students to perform hydrologic calculations related to rainfall measurement, runoff estimation and unit hydrograph development.
This document discusses precipitation and methods of measuring precipitation. It defines precipitation as moisture falling from the atmosphere in any form. The key forms of precipitation are liquid (rain, drizzle) and frozen (snow, hail, sleet). Precipitation is measured using various devices like rain gauges and satellites. Rain gauges include non-recording and recording types like tipping bucket gauges. Methods to calculate average precipitation over an area include arithmetic averages, Thiessen polygons, and isohyetal mapping. Factors influencing precipitation amounts are also examined.
This document discusses laminar and turbulent fluid flow in pipes. It defines the Reynolds number and explains that laminar flow occurs at Re < 2000, transitional flow from 2000 to 4000, and turbulent flow over 4000. The entrance length for developing pipe flow profiles is discussed. Fully developed laminar and turbulent pipe flows are compared. Equations are provided for average velocity, shear stress at the wall, and pressure drop based on conservation of momentum and energy analyses. The Darcy friction factor is defined, and methods for calculating it for laminar and turbulent flows are explained, including the Moody chart. Types of pipe flow problems and accounting for minor losses and pipe networks are also summarized.
This document discusses different types of notches and weirs used for measuring flow rates of liquids. It provides formulas to calculate discharge over rectangular, triangular, trapezoidal, broad crested, narrow crested, and submerged/drowned weirs. Key points include: discharge over a triangular notch or weir is given by Q=8/15Cd tan(θ/2)√2gH(5/2); a broad crested weir has a width at least twice the head and discharge is maximized at Qmax=1.705CdL√2gH(3/2); submerged weirs are divided into a free section and drowned section to calculate total discharge.
- Open channel flow occurs in natural settings like rivers and streams as well as human-made channels. It is characterized by a free surface boundary.
- Flow can be uniform, gradually varied, or rapidly varied depending on changes in depth and velocity over distance. Uniform flow maintains constant depth and velocity.
- Important parameters include the Froude number, specific energy, and wave speed. Hydraulic jumps and critical flow occur when the Froude number is 1.
- Flow is controlled using underflow gates, overflow gates, and weirs. Measurement relies on critical flow assumptions at weirs.
The document describes procedures for determining the liquid limit and plastic limit of soil samples. The liquid limit test involves adding water to soil and determining the moisture content at which a groove closes after 25 blows. The plastic limit is the moisture content at which a soil ball crumbles after rolling out to 3mm diameter. These limits are used to classify soils and predict properties like strength and compressibility. The plasticity index, defined as the liquid limit minus the plastic limit, provides further information on soil type and reactivity. Proper determination of the Atterberg limits is important for building foundations to ensure suitable shear strength and volume change with moisture fluctuations.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
lab 4 requermenrt.pdf
MECH202 – Fluid Mechanics – 2015 Lab 4
Fluid Friction Loss
Introduction
In this experiment you will investigate the relationship between head loss due to fluid friction and
velocity for flow of water through both smooth and rough pipes. To do this you will:
1) Express the mathematical relationship between head loss and flow velocity
2) Compare measured and calculated head losses
3) Estimate unknown pipe roughness
Background
When a fluid is flowing through a pipe, it experiences some resistance due to shear stresses, which
converts some of its energy into unwanted heat. Energy loss through friction is referred to as “head
loss due to friction” and is a function of the; pipe length, pipe diameter, mean flow velocity,
properties of the fluid and roughness of the pipe (the later only being a factor for turbulent flows),
but is independent of pressure under with which the water flows. Mathematically, for a turbulent
flow, this can be expressed as:
hL=f
L
D
V
2
2 g
(Eq.1)
where
hL = Head loss due to friction (m)
f = Friction factor
L = Length of pipe (m)
V = Average flow velocity (m/s)
g = Gravitational acceleration (m/s^2)
Friction head losses in straight pipes of different sizes can be investigated over a wide range of
Reynolds' numbers to cover the laminar, transitional, and turbulent flow regimes in smooth pipes. A
further test pipe is artificially roughened and, at the higher Reynolds' numbers, shows a clear
departure from typical smooth bore pipe characteristics.
Experiment 4: Fluid Friction Loss
The head loss and flow velocity can also be expressed as:
1) hL∝V −whe n flow islaminar
2) hL∝V
n
−whe n flow isturbulent
where hL is the head loss due to friction and V is the fluid velocity. These two types of flow are
seperated by a trasition phase where no definite relationship between hL and V exist. Graphs
of hL −V and log (hL) − log (V ) are shown in Figure 1,
Figure 1. Relationship between hL ( expressed by h) and V ( expressed by u ) ;
as well as log (hL) and log ( V )
Experiment 4: Fluid Friction Loss
Experimental Apparatus
In Figure 2, the fluid friction apparatus is shown on the right while the Hydraulic bench that
supplies the water to the fluid friction apparatus is shown on the left. The flow rate that the
hydraulic bench provides can be measured by measuring the time required to collect a known
volume.
Figure 2. Experimental Apparatus
Experimental Procedure
1) Prime the pipe network with water by running the system until no air appears to be discharging
from the fluid friction apparatus.
2) Open and close the appropriate valves to obtain water flow through the required test pipe, the four
lowest pipes of the fluid friction apparatus will be used for this experiment. From the bottom to the
top, these are; the rough pipe with large diameter and then smooth pipes with three successively
smaller diameters.
3) Measure head loss ...
Fluid Mechanics Chapter 3. Integral relations for a control volumeAddisu Dagne Zegeye
Introduction, physical laws of fluid mechanics, the Reynolds transport theorem, Conservation of mass equation, Linear momentum equation, Angular momentum equation, Energy equation, Bernoulli equation
WATER RESOURCES ENGINEERING MODULE 1 NOTESReshmaMRaju
This document provides an overview of key concepts in hydrology and water resources engineering. It discusses the hydrologic cycle and its three main processes of evaporation, precipitation, and runoff. It describes different types of precipitation including cyclonic, convective, and orographic precipitation. Measurement of rainfall using rain gauges is also summarized, including factors to consider for the optimal number of rain gauges. Methods for estimating missing precipitation data from nearby rain gauges are outlined, such as the arithmetic mean method, normal ratio method, and inverse distance method.
The document provides design steps for a canal drop-notch structure. Key steps include:
1) Designing the trapezoidal notch including the number of notches, bottom width, and side slopes based on upstream and downstream water levels.
2) Designing the drop wall with appropriate thickness, height, and bottom width to safely convey water over the notch.
3) Designing a water cushion cistern downstream of the notch using Bligh's creep theory to determine adequate thickness to prevent uplift.
4) Designing protective works including abutments, wing walls, and revetment pitching upstream and downstream for structural integrity and erosion protection.
This document discusses local energy (head) losses that occur in pipes due to changes in pipe geometry or flow direction. It introduces minor losses that are proportional to the velocity head and defined by a loss coefficient. Specific minor losses are examined for abrupt enlargements and contractions using the continuity, momentum, and Bernoulli equations. Loss coefficients are determined experimentally and provided in tables based on the area ratio. The total head loss in a pipe system is calculated considering losses at the pipe entrance/exit and along the length. Local losses are generally negligible for long pipes.
This chapter discusses energy losses that occur in pipe networks due to fluid flow. It describes major losses, which are primarily due to friction within the pipe, and minor losses, which are secondary losses caused by changes in pipe diameter, bends, valves, and other components. Methods are provided to calculate the head loss associated with major and minor losses using equations that consider factors like pipe roughness, diameter, flow rate, and geometry of components. Worked examples are also included to demonstrate calculating head losses in pipe networks with pipes arranged in series and parallel configurations.
This document provides an introduction to hydrology, including:
1. Hydrology is defined as the science of water, its occurrence and circulation on Earth. It deals with water resources, processes like precipitation and runoff, and problems like floods and droughts.
2. The hydrologic cycle describes the continuous movement of water on, above, and below the Earth's surface, including evaporation, transpiration, precipitation, runoff, and storage components.
3. The water budget equation expresses the relationship between inputs, outputs, and changes in storage of water in a given catchment area over a period of time.
1. The document describes an experiment conducted to determine hydrostatic pressure and the center of pressure acting on a plane surface using a hydrostatic pressure apparatus.
2. The experiment involved setting the apparatus at an angle, balancing it by adding weights, and measuring the water level as more weights were added.
3. Calculations were done to find theoretical and practical hydrostatic pressures using equations for the area, height, resultant force, and center of pressure. The results showed some difference between theoretical and practical pressures.
This document describes an experiment to verify the momentum equation through measuring the impact of a water jet. The objective is to experimentally test Newton's second law of motion as it applies to fluid momentum. The apparatus required includes an impact of jet setup, weights, and a stopwatch. The theoretical basis is explained, noting that the sum of external forces equals the rate of change of momentum. The experimental setup and procedure are outlined, involving measuring the discharge and velocity of the jet using a collecting tank and nozzle, and determining the force on a target plate by adding weights to return it to its initial position. Observations are recorded for different flow rates.
The document discusses concepts related to fluid flow including continuity equations, conservation of mass, Bernoulli's equation, and venturi meters. It provides examples of calculating volume flow rate, fluid velocity, mass flow rate, and pressure given pipe dimensions and fluid properties. It also discusses how venturi meters can be used to measure flow rates based on pressure changes through the converging and diverging sections.
this is the experiment of fluid mechanics .FLOW OVER A SHARP CRESTED WEIR.experiment of weir.from this experiment we can learn discharge over the sharp crested weir and etc.
This document contains 43 questions related to hydrology and water resources engineering. The questions cover topics like the hydrologic cycle, precipitation, rainfall measurement, runoff analysis, unit hydrographs, flood frequency analysis and flood routing. Most of the questions ask students to explain hydrologic concepts, factors affecting runoff and infiltration, methods to derive unit hydrographs and questions related to flood estimation. A few questions ask students to perform hydrologic calculations related to rainfall measurement, runoff estimation and unit hydrograph development.
This document discusses precipitation and methods of measuring precipitation. It defines precipitation as moisture falling from the atmosphere in any form. The key forms of precipitation are liquid (rain, drizzle) and frozen (snow, hail, sleet). Precipitation is measured using various devices like rain gauges and satellites. Rain gauges include non-recording and recording types like tipping bucket gauges. Methods to calculate average precipitation over an area include arithmetic averages, Thiessen polygons, and isohyetal mapping. Factors influencing precipitation amounts are also examined.
This document discusses laminar and turbulent fluid flow in pipes. It defines the Reynolds number and explains that laminar flow occurs at Re < 2000, transitional flow from 2000 to 4000, and turbulent flow over 4000. The entrance length for developing pipe flow profiles is discussed. Fully developed laminar and turbulent pipe flows are compared. Equations are provided for average velocity, shear stress at the wall, and pressure drop based on conservation of momentum and energy analyses. The Darcy friction factor is defined, and methods for calculating it for laminar and turbulent flows are explained, including the Moody chart. Types of pipe flow problems and accounting for minor losses and pipe networks are also summarized.
This document discusses different types of notches and weirs used for measuring flow rates of liquids. It provides formulas to calculate discharge over rectangular, triangular, trapezoidal, broad crested, narrow crested, and submerged/drowned weirs. Key points include: discharge over a triangular notch or weir is given by Q=8/15Cd tan(θ/2)√2gH(5/2); a broad crested weir has a width at least twice the head and discharge is maximized at Qmax=1.705CdL√2gH(3/2); submerged weirs are divided into a free section and drowned section to calculate total discharge.
- Open channel flow occurs in natural settings like rivers and streams as well as human-made channels. It is characterized by a free surface boundary.
- Flow can be uniform, gradually varied, or rapidly varied depending on changes in depth and velocity over distance. Uniform flow maintains constant depth and velocity.
- Important parameters include the Froude number, specific energy, and wave speed. Hydraulic jumps and critical flow occur when the Froude number is 1.
- Flow is controlled using underflow gates, overflow gates, and weirs. Measurement relies on critical flow assumptions at weirs.
The document describes procedures for determining the liquid limit and plastic limit of soil samples. The liquid limit test involves adding water to soil and determining the moisture content at which a groove closes after 25 blows. The plastic limit is the moisture content at which a soil ball crumbles after rolling out to 3mm diameter. These limits are used to classify soils and predict properties like strength and compressibility. The plasticity index, defined as the liquid limit minus the plastic limit, provides further information on soil type and reactivity. Proper determination of the Atterberg limits is important for building foundations to ensure suitable shear strength and volume change with moisture fluctuations.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
lab 4 requermenrt.pdf
MECH202 – Fluid Mechanics – 2015 Lab 4
Fluid Friction Loss
Introduction
In this experiment you will investigate the relationship between head loss due to fluid friction and
velocity for flow of water through both smooth and rough pipes. To do this you will:
1) Express the mathematical relationship between head loss and flow velocity
2) Compare measured and calculated head losses
3) Estimate unknown pipe roughness
Background
When a fluid is flowing through a pipe, it experiences some resistance due to shear stresses, which
converts some of its energy into unwanted heat. Energy loss through friction is referred to as “head
loss due to friction” and is a function of the; pipe length, pipe diameter, mean flow velocity,
properties of the fluid and roughness of the pipe (the later only being a factor for turbulent flows),
but is independent of pressure under with which the water flows. Mathematically, for a turbulent
flow, this can be expressed as:
hL=f
L
D
V
2
2 g
(Eq.1)
where
hL = Head loss due to friction (m)
f = Friction factor
L = Length of pipe (m)
V = Average flow velocity (m/s)
g = Gravitational acceleration (m/s^2)
Friction head losses in straight pipes of different sizes can be investigated over a wide range of
Reynolds' numbers to cover the laminar, transitional, and turbulent flow regimes in smooth pipes. A
further test pipe is artificially roughened and, at the higher Reynolds' numbers, shows a clear
departure from typical smooth bore pipe characteristics.
Experiment 4: Fluid Friction Loss
The head loss and flow velocity can also be expressed as:
1) hL∝V −whe n flow islaminar
2) hL∝V
n
−whe n flow isturbulent
where hL is the head loss due to friction and V is the fluid velocity. These two types of flow are
seperated by a trasition phase where no definite relationship between hL and V exist. Graphs
of hL −V and log (hL) − log (V ) are shown in Figure 1,
Figure 1. Relationship between hL ( expressed by h) and V ( expressed by u ) ;
as well as log (hL) and log ( V )
Experiment 4: Fluid Friction Loss
Experimental Apparatus
In Figure 2, the fluid friction apparatus is shown on the right while the Hydraulic bench that
supplies the water to the fluid friction apparatus is shown on the left. The flow rate that the
hydraulic bench provides can be measured by measuring the time required to collect a known
volume.
Figure 2. Experimental Apparatus
Experimental Procedure
1) Prime the pipe network with water by running the system until no air appears to be discharging
from the fluid friction apparatus.
2) Open and close the appropriate valves to obtain water flow through the required test pipe, the four
lowest pipes of the fluid friction apparatus will be used for this experiment. From the bottom to the
top, these are; the rough pipe with large diameter and then smooth pipes with three successively
smaller diameters.
3) Measure head loss ...
Fluid Mechanics Chapter 3. Integral relations for a control volumeAddisu Dagne Zegeye
Introduction, physical laws of fluid mechanics, the Reynolds transport theorem, Conservation of mass equation, Linear momentum equation, Angular momentum equation, Energy equation, Bernoulli equation
This document provides an introduction and overview of a thesis investigating minor water loss and head loss coefficients in locally available PVC pipes with 90-degree bends of different dimensions. It discusses the purpose of determining minor loss coefficients for local pipes, which are not currently available. The document outlines previous related works and the structure of the thesis, which will present experimental results and findings to help establish more convenient use of local pipes in local industries.
This document describes an experiment conducted to determine the friction factor of water flowing through a pipe. The experiment measured the volumetric flow rate, velocity, temperature, and pressure drop of water flowing through a pipe. These measurements were used to calculate the Reynolds number, theoretical friction factor based on equations, and experimental friction factor. The results showed that at higher Reynolds numbers, the friction factor was lower, following trends in friction factor charts. Sources of error included inaccurate measurements of pressure drop and flow time. The experiment demonstrated how friction factor depends inversely on Reynolds number for turbulent flow in a pipe.
Rev. August 2014 ME495 - Pipe Flow Characteristics… Page .docxjoyjonna282
Rev. August 2014 ME495 - Pipe Flow Characteristics… Page 2
2
ME495—Thermo Fluids Laboratory
~~~~~~~~~~~~~~
PIPE FLOW CHARACTERISTICS
AND PRESSURE TRANSDUCER
CALIBRATION
~~~~~~~~~~~~~~
PREPARED BY: GROUP LEADER’S NAME
LAB PARTNERS: NAME
NAME
NAME
TIME/DATE OF EXPERIMENT: TIME , DATE
~~~~~~~~~~~~~~
OBJECTIVE— The objectives of this experiment are
to: a) observe the characteristics of flow in a pipe,
b) evaluate the flow rate in a pipe using velocity
and pressure difference measurements, and c)
perform the calibration of a pressure transducer.
Upon completing this experiment you should have
learned (i) how to measure the flow rate and average
velocity in a pipe using a Pitot tube and/or a resistance
flow meter, and (ii) how to classify the general
characteristics of a pipe flow.
Nomenclature
a = speed of sound, m/s
A = area, m
2
C = discharge coefficient, dimensionless
d = pipe diameter, m
d0 = orifice diameter, m
E = velocity approach factor, dimensionless
f = Darcy friction factor, dimensionless
K0 = flow coefficient, dimensionless
k = ratio of specific heats (cp/cv), dimensionless
L = length of pipe, m
M = Mach number, dimensionless
p = pressure, Pa
p0 = stagnation pressure, Pa
p1, p2 = pressure at two axial locations along a
pipe, Pa
Q = volumetric flow rate, m
3
/s
R = specific gas constant, J·kg/K
Re = Reynolds number, dimensionless
T = temperature, K
V = local velocity, m/s
V = average velocity, m/s
Y = adiabatic expansion factor, dimensionless
= ratio of orifice diameter to pipe diameter,
dimensionless
p = pressure drop across an orifice meter, Pa
= dynamic viscosity, Pa·s
= air density, kg/m3
INTRODUCTION— The flow of a fluid (liquid or
gas) through pipes or ducts is a common part of many
engineering systems. Household applications include
the flow of water in copper pipes, the flow of natural
gas in steel pipes, and the flow of heated air through
metal ducts of rectangular cross-section in a forced-air
furnace system. Industrial applications range from the
flow of liquid plastics in a manufacturing plant, to the
flow of yogurt in a food-processing plant. Because the
purpose of a piping system is to transport a desired
quantity of fluid, it is important to understand the
various methods of measuring the flow rate.
In order to work with a fluid system, and certainly to
design a fluid system that will deliver a prescribed
flow, it is necessary to understand certain fundamental
aspects of the fluid flow. For this, one should be able
to answer questions like: Are compressibility effects
important? Is the flow laminar or turbulent? Is the
viscosity of the fluid important or not? Is the flow
steady or varying with time? What are the primary
forces of importance? For internal ...
This document discusses fluid flow, including laminar and turbulent flow, transition between the two, and the effects of turbulence. It also covers topics like pipe flow, the Reynolds number parameter, and pressure drops and head losses in pipes. Some key points made include:
- At moderate Reynolds numbers, smooth laminar flow becomes fluctuating turbulent flow due to transition.
- Turbulence enhances heat and mass transfer compared to laminar flow.
- Fully developed pipe flow can be modeled using logarithmic velocity profiles and relationships between friction factor and Reynolds number.
- Minor losses from fittings add to overall pressure drops beyond just major losses in straight pipe sections.
Report on Types of fluid flow
fluid dynamics
Introduction
In physics, fluid flow has all kinds of aspects: steady or unsteady, compressible or incompressible, viscous or non-viscous, and rotational or irrotational to name a few. Some of these characteristics reflect properties of the liquid itself, and others focus on how the fluid is moving. Note that fluid flow can get very complex when it becomes turbulent. Physicists haven’t developed any elegant equations to describe turbulence because how turbulence works depends on the individual system whether you have water cascading through a pipe or air streaming out of a jet engine. Usually, you have to resort to computers to handle problems that involve fluid turbulence. Types of fluid flow:
Aerodynamic force
Cavitation
Compressible flow
Couette flow
Free molecular flow
Incompressible flow
The document summarizes an experimental investigation into fluid elastic instability in cross-flow shell and tube heat exchanger bundles. The study aims to compare vibration results for triangular and square tube bundle arrays and examine how parameters like mass-damping, tube frequency, and critical fluid velocity are influenced. Testing will be done on a experimental setup with a test section subjected to partial liquid water flow. The expected results are minimized flow-induced vibrations in the tube bundle during non-uniform cross-flow. Utilization of the results could help identify more influenced parameters and vibration modes at different critical velocities to reduce failures in heat exchangers.
This document describes a computational fluid dynamics (CFD) simulation of laminar flow in a pipe using ANSYS software. The summary is:
1. The simulation setup involved modeling the pipe geometry, generating a fine mesh, defining boundary conditions for the inlet and outlet, and running the simulation for 1000 iterations.
2. The results showed the classic parabolic velocity profile and gradual pressure drop associated with laminar flow.
3. The orderly and predictable behavior of laminar flow was observed, highlighting its energy-efficient properties important for applications like fluid transport systems.
This document discusses energy losses that occur in hydraulic systems. It begins by defining laminar and turbulent flows, and introduces the Reynolds number which determines the type of flow. It then explains that greater energy losses occur in turbulent flow compared to laminar flow. The document goes on to describe the Darcy-Weisbach equation for calculating head losses due to friction in pipes. Specific equations are provided to calculate losses for laminar and turbulent flow, taking into account factors like pipe roughness and Reynolds number. The purpose is to analyze energy losses that occur in components like valves and fittings so they can be properly accounted for in system design.
Friction losses in turbulent flow (Fanning Equation).pdfSharpmark256
This document discusses fluid flow in pipes, including laminar and turbulent flow regimes. It defines key terms like Reynolds number, friction factor, pressure drop, and boundary layers. For laminar flow, the friction factor can be predicted from the Reynolds number using theoretical equations. For turbulent flow, the friction factor must be determined experimentally and depends on both the Reynolds number and pipe roughness.
This publication is intended for engineers seeking an introduction to the problem of water hammer in pumped pressure mains. This is a subject of increasing interest because of the development of larger and more integrated sewer systems. Consideration of water hammer is essential for structural design of pipelines.
IRJET- Analysis of Two Phase Flow Induced Vibration in Piping SystemsIRJET Journal
1. The document analyzes two-phase flow induced vibration in piping systems. It develops the governing dynamic equation and stiffness/inertia matrices for a pipe conveying fluid.
2. Four boundary conditions are considered: pinned-pinned, clamped-pinned, clamped-clamped, and clamped-free. Analytical and finite element methods are used to find natural frequencies under different conditions.
3. Pipe buckling or divergence is observed at higher fluid velocities for some boundary conditions. The critical velocity at which buckling starts is identified. Natural frequency diminishes at the onset of divergence for some cases.
This document summarizes a study on the impact of increasing depth and diameter on flow regime transition in deepwater flowlines and risers. The study involved simulating a typical deepwater oil field in West Africa over 1000m depth using OLGA simulations. Sensitivity analysis was carried out to simulate the impact of increasing depth to 2000m and 3000m, and increasing diameter to 12 inches and 16 inches. Preliminary results showed transition to slug flow for low mass flowrates of less than 3000 bopd at a water-cut of 30% for the 8-inch baseline case. Increasing diameter and depth appeared to increase slugging tendency, with transition occurring between the riser base and topsides. Further simulations are being carried out to
Pipe corrosion is caused by several factors related to water chemistry and physical properties. Low pH, high oxygen content, carbon dioxide, and bacteria can all promote corrosion by speeding up the electrochemical oxidation process. Water temperature also affects corrosion rates, with higher temperatures generally causing faster corrosion. Physical factors like flow turbulence at locations with sudden changes in direction can lead to erosion corrosion. Galvanic corrosion can occur when dissimilar metals are in contact within the piping system. Proper material selection and water treatment can help reduce corrosion in pipe lines.
Comparative CFD and Simulative Analysis of Flow Behaviour to Calculate Losses...ijtsrd
The document presents a comparative analysis of computational fluid dynamics (CFD) and simulation to calculate fluid flow losses in pipes of different geometries. Three techniques are used and compared - experimental testing, virtual lab simulation, and ANSYS Fluent CFD software. The major findings are that CFD results using ANSYS Fluent are most accurate and precise compared to experimental and virtual lab results, as CFD is not subject to experimental errors. CFD can also be easily modified for different pipe geometries and flow conditions. The study provides a basis for selecting the most effective method of calculating fluid flow losses in pipes.
Cavitation in Francis turbines negatively impacts performance and causes damage. It occurs when pressure drops below vapor pressure, forming bubbles that collapse upon reaching higher pressure zones. This results in pitting on turbine surfaces from high localized pressures. Remedies include optimizing hydraulic design to reduce cavitation, and developing coatings for wetted parts to prolong maintenance intervals. Cavitation repair involves welding or spraying metallic/non-metallic coatings, with some coatings showing better erosion resistance than stainless steel. Preventing cavitation requires correct turbine design, manufacturing quality, material selection, installation, operation, maintenance, and supplemental air injection into the draft tube.
The document discusses the fundamental principles of fluid mechanics - conservation of mass, energy, and momentum - and how they are applied to derive equations for open channel flow. It specifically covers the continuity, energy, and momentum equations. The energy equation relates changes in energy within a control volume, while the momentum equation relates the overall forces on the control volume boundaries. The document also discusses topics like specific energy, critical flow, hydraulic jumps, and how these concepts are used to analyze channel transitions and design channel flows.
Flow-induced vibration in heat exchangers has been a major problem for decades. Three main mechanisms that cause vibration are fluid-elastic instability, vortex shedding, and multi-phase buffeting. Fluid-elastic instability is the most important mechanism for shell and tube heat exchangers. Several studies have analyzed vibration experimentally and through computational fluid dynamics simulations. Parameters like damping ratios, tube properties, fluid properties, and flow velocities are important factors in vibration analysis and predicting the onset of instability.
The document describes a study that investigated the depth-wise profiles of velocity and turbulence parameters in the proximity of a mid-channel bar using experimental and computational fluid dynamics (CFD) modeling methods. Velocity measurements were taken at various depths and locations near the mid-channel bar using an acoustic Doppler velocimeter (ADV). The study found changes in the velocity and turbulence profiles due to interactions between the fluid flow and the mid-channel bar. CFD modeling with the Reynolds stress model was also used to validate the experimental results.
PRODUCTION OPTIMIZATION ASSESSMENT USING THAI, AND VAPEX EOR METHODS BY USING...Mahmood Ajabbar
Nowadays the energy sources generation is getting more difficult by using the enhanced and advanced level of technology around the world and as non-renewable energy oil and gas industries have become the largest and most demanded supplements of energy generation.
In brief, this project utilizes two types of EOR methods which use to produce heavy oil. The first method is the TAHI method which use steam to reduce the viscosity. The second method is the VAPEX method which use solvent to produce the heavy oil with economical way and friendly environment. It has bee got the RF for VAPEX IS around 62%, and for THAI is 71%. After comparing the both results in term of ability, now will compared it in terms of economics, the THAI method has profit which is 211.96×10^6 Dollars, and the VAPEX method is around 184.04×10^6$. So, the best method for this reservoir is the THAI method.
ABSTRACT
The assignment outlines the professional codes of conduct relevant to BEM and adhered by professional engineers who serve to the society considering or exhibiting with legal, safety health, cultural and societal values. A certified professional engineer holds high dignity, ethics, professional, moral values in making decisions at the place of work. The main objective of this assignment is to examine, analyze and relate the ethical theories and the BEM (Board of Engineers Malaysia) Code of Professional Conduct and its guidelines to solve ethical, social, health, safety, legal, and cultural related issues in the practice of engineering in order to safe guard the respect and dignity of the Engineering Profession. Furthermore; in this assignment will learn about the ethical theory which use to reduce the impact inside the industry, as we learned there five elements of the ethics theory will be used to evaluate and analyze the cases study below in chapter two, those elements are Relativism, Utilitarianism, Virtue Ethics, Duty Ethics, and Right Ethics each one of these will be used in the scenarios below. Moreover; in this assignment will explain some codes of the BEM codes of Professional Conduct, this code consists of five elements which will mention in chapter3 each one of these codes divided into various codes to be used as a professional engineer to solve the issues which may face. In addition, will be selecting some of the BEM codes to solve the issue base on the problems which we have in chapter 2, there three case study each case study has different problems, furthermore, the last case study is the scenario which is given in the assignment to be analyzed. As a professional engineer must solve this issue by justify the solution for the case study and make sure there is no impact on the capacity and environment. Furthermore; will be using the drawing line analysis to identify the impact of the problems, as shown in chapter 3 there are a positive impact and negative impact by using this method we can identify if the problems are negative or positive then will solve this issue.
BIT HYDRAULICS ANALYSIS FOR EFFICIENT HOLE CLEANINGMahmood Ajabbar
Abstract
This project was helpful for the student to get knowledge in general about the petroleum engineer and how to calculate the pressure loss of the system as well as the section of the optimum nozzle for the drill bit this assignment will help a lot the drilling engineer in future. Furthermore, this project helps to solve the challenges that faced the petroleum engineer in real life. However, in this project, the student learned how to deal with errors and converted to the advantage and overcome with better results. From the given data the optimum mud flow rates and the nozzle sizes should be designed for drilling at various depths until the end of the section. The nozzle areas of hydraulics horsepower for surface casing was 0.27 〖in〗^2, and for the intermediate casing are 0.23〖in〗^2 and 0,17〖in〗^2, and the last optimum nozzle area for the production which has been calculated is 0.2〖in〗^2. Last but not less this assignment was helpful l for students to get knowledge about drilling hydraulics. Nozzle configuration appears to have an effect on penetration rate. Several authors have described improved drill rates with extended or blanked nozzle bits. However, presently used criteria have been unable to account for these improved drill rates. in fact, has suggested a different optimum may exist for each nozzle size. Drill cuttings in the wellbore cause wear and tear to the drill string and this reduces the rate of penetration; therefore, there is a need for efficient bottom hole cleaning. During a drilling operation, optimization of hydraulic horsepower at the drill bit is adopted to enhance bottom hole cleaning and to increase the rate of penetration. Optimum drilling conditions are achieved using either the maximum horsepower criterion or the hydraulic jet impact force criterion.
Abstract:
This assignment was used to design a mud and preparing mud for a well having a depth of 10000ft and each depth consist of different pore pressure gradient and fracture gradient. It was important to take in consider the safety margins and the kick margins by adding to the pore pressure gradient 0.5ppg and subtracting from fracture pressure 0.5ppg as shown in table (1). Then it has been drew the mud window to create a proper mud to solve the issue in this assignment and become safer. Since there are two muds needed to be prepared for a well having a depth of 10000ft and each with different density, it is important to measure the amount of barite required in order to increase the density to the target wanted. has been created the mud with 10.9 ppg, after creating the mud for this density will be testing all the classification for this test and if it is goof or no. The temperature for this mud was 28.7C and the density has been measured as well which was 10.95 and the ph was 8. In addition, has been measured the viscosity at different speed by using viscometers the speed was at 5,6,100,200,300, and 600 rpm the results shows in table 3. Then it has been measured the gel strength at 10s and 10 mins which was 30, and 31ib.100ft2 respectively, then it has been calculated the plastic viscosity, apparent viscosity, and yield point by the equation given above, and the results mentioned in table 3. Lastly has been measure the filtrate volume for 5,10, 15,20,15 and 30mins the total volume which was at 30 mins with result about 16.5cc. then it has been measured the mud cake thickness for this type of mud which was 3.23mm. it was given some of the errors that faced while drilling a well, those problems were loss circulation, high and innovation and the stuck pipe. in the first step it has been designed the sample mud that required to use at the surface, while the pressure of the well increase it should increase the density of the mud to balance between the hydrostatic pressure with the formation pressure, so it has been increased the density of the mud by using the barite, the mud was 10, and 14ppg.
1. The document discusses a study on the effect of contamination on water-based drilling mud. Salt (NaCl) was added to fresh water mud at 0.1% to study its effects.
2. Testing found that adding NaCl increased the mud density to 9.08 ppg and maintained a pH of 8. Filtrate volume was measured at 22 cc after 30 minutes. Mud cake thickness was recorded as 3.42 mm.
3. The plastic viscosity was 6 cP, apparent viscosity was 20 cP, and yield point was 28 lb/100ft2. Gel strengths were 30 lb/100ft2 at 10 seconds and 31 lb/100ft2 at 10 minutes.
Abstract
The aim of this experiment is to study the properties of loss control additives and its effect towards mud properties and to test what different additives do to the behaviour of drilling mud in terms of mud cake formation and filtrate loss. Guar gum has been used extensively in the oil industry as a viscosity for different applications due to its unique rheological properties. In this paper, we explore how the rheological behaviour of guar-based fluids can be used to control fluid loss. a range of instruments were used such Mud mixer, Mud balance, Thermometer, Remoter, Filter press, Graduated cylinder, pH meter / pH paper, Aging cell, Rotating oven and litter cup, Viscometer and Venire calliper. All these materials were used in order to understand the reasons why the mud varies and to know with precision the different properties that the fluids have. overall, at this experiment was conducted by using Bentonite of 15g, soda ash of 0.2g and guar gum of 0.3g mixed with water of 350ml to control the fluid loss of the mud. After that compare the results of experiment 1 with experiment 4.
ABSTRACT
This experiment examined the effect of mud thinner on drilling fluid density and viscosity. The function of mud thinner is to control and reduce the apparent density of the mud by calculate the amount of water that needed to decrease the density. The experiment was conducted by using one basic mud as the comparison for second experiment that has 10.7ppg mud density, then it uses mud thinner to achieve the exact mud density that required in this experiment which is 10.2ppg. Also, this experiment was undertaken with the purpose of decrease the density of the drilling fluid as well as to measure the properties of the drilling fluids and compare it with the last experiment. In general, to proceed with the experiment in order to achieve the goals mentioned, a range of instruments were selected such Mud mixer, Mud balance, Thermometer, Remoter, Filter press, Graduated cylinder, pH meter / pH paper, Aging cell, Rotating oven and litter cup, Viscometer and Venire calliper. All these materials were used in order to understand the reasons why the mud varies and to know with precision the different properties that the fluids have. overall, at this experiment was conducted by using Bentonite, Barite and soda ash mixed with water to control the density of the mud.
The field development plan aims to maximize oil recovery from the Sirri-A oil field located offshore Iran. Key objectives include developing a reservoir model, evaluating development strategies, and determining cash flows. The reservoir is a limestone formation from the Cretaceous period. Analysis shows it has an initial oil in place of 1.78 billion stock tank barrels and is primarily driven by water. Development scenarios include a base case, increased well counts, secondary water injection, and tertiary WAG injection. The WAG scenario recovers an estimated 52.3% of the oil in place.
ACEP Magazine edition 4th launched on 05.06.2024Rahul
This document provides information about the third edition of the magazine "Sthapatya" published by the Association of Civil Engineers (Practicing) Aurangabad. It includes messages from current and past presidents of ACEP, memories and photos from past ACEP events, information on life time achievement awards given by ACEP, and a technical article on concrete maintenance, repairs and strengthening. The document highlights activities of ACEP and provides a technical educational article for members.
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressionsVictor Morales
K8sGPT is a tool that analyzes and diagnoses Kubernetes clusters. This presentation was used to share the requirements and dependencies to deploy K8sGPT in a local environment.
International Conference on NLP, Artificial Intelligence, Machine Learning an...gerogepatton
International Conference on NLP, Artificial Intelligence, Machine Learning and Applications (NLAIM 2024) offers a premier global platform for exchanging insights and findings in the theory, methodology, and applications of NLP, Artificial Intelligence, Machine Learning, and their applications. The conference seeks substantial contributions across all key domains of NLP, Artificial Intelligence, Machine Learning, and their practical applications, aiming to foster both theoretical advancements and real-world implementations. With a focus on facilitating collaboration between researchers and practitioners from academia and industry, the conference serves as a nexus for sharing the latest developments in the field.
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECTjpsjournal1
The rivalry between prominent international actors for dominance over Central Asia's hydrocarbon
reserves and the ancient silk trade route, along with China's diplomatic endeavours in the area, has been
referred to as the "New Great Game." This research centres on the power struggle, considering
geopolitical, geostrategic, and geoeconomic variables. Topics including trade, political hegemony, oil
politics, and conventional and nontraditional security are all explored and explained by the researcher.
Using Mackinder's Heartland, Spykman Rimland, and Hegemonic Stability theories, examines China's role
in Central Asia. This study adheres to the empirical epistemological method and has taken care of
objectivity. This study analyze primary and secondary research documents critically to elaborate role of
china’s geo economic outreach in central Asian countries and its future prospect. China is thriving in trade,
pipeline politics, and winning states, according to this study, thanks to important instruments like the
Shanghai Cooperation Organisation and the Belt and Road Economic Initiative. According to this study,
China is seeing significant success in commerce, pipeline politics, and gaining influence on other
governments. This success may be attributed to the effective utilisation of key tools such as the Shanghai
Cooperation Organisation and the Belt and Road Economic Initiative.
Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024Sinan KOZAK
Sinan from the Delivery Hero mobile infrastructure engineering team shares a deep dive into performance acceleration with Gradle build cache optimizations. Sinan shares their journey into solving complex build-cache problems that affect Gradle builds. By understanding the challenges and solutions found in our journey, we aim to demonstrate the possibilities for faster builds. The case study reveals how overlapping outputs and cache misconfigurations led to significant increases in build times, especially as the project scaled up with numerous modules using Paparazzi tests. The journey from diagnosing to defeating cache issues offers invaluable lessons on maintaining cache integrity without sacrificing functionality.
Comparative analysis between traditional aquaponics and reconstructed aquapon...bijceesjournal
The aquaponic system of planting is a method that does not require soil usage. It is a method that only needs water, fish, lava rocks (a substitute for soil), and plants. Aquaponic systems are sustainable and environmentally friendly. Its use not only helps to plant in small spaces but also helps reduce artificial chemical use and minimizes excess water use, as aquaponics consumes 90% less water than soil-based gardening. The study applied a descriptive and experimental design to assess and compare conventional and reconstructed aquaponic methods for reproducing tomatoes. The researchers created an observation checklist to determine the significant factors of the study. The study aims to determine the significant difference between traditional aquaponics and reconstructed aquaponics systems propagating tomatoes in terms of height, weight, girth, and number of fruits. The reconstructed aquaponics system’s higher growth yield results in a much more nourished crop than the traditional aquaponics system. It is superior in its number of fruits, height, weight, and girth measurement. Moreover, the reconstructed aquaponics system is proven to eliminate all the hindrances present in the traditional aquaponics system, which are overcrowding of fish, algae growth, pest problems, contaminated water, and dead fish.
Advanced control scheme of doubly fed induction generator for wind turbine us...IJECEIAES
This paper describes a speed control device for generating electrical energy on an electricity network based on the doubly fed induction generator (DFIG) used for wind power conversion systems. At first, a double-fed induction generator model was constructed. A control law is formulated to govern the flow of energy between the stator of a DFIG and the energy network using three types of controllers: proportional integral (PI), sliding mode controller (SMC) and second order sliding mode controller (SOSMC). Their different results in terms of power reference tracking, reaction to unexpected speed fluctuations, sensitivity to perturbations, and resilience against machine parameter alterations are compared. MATLAB/Simulink was used to conduct the simulations for the preceding study. Multiple simulations have shown very satisfying results, and the investigations demonstrate the efficacy and power-enhancing capabilities of the suggested control system.
Understanding Inductive Bias in Machine LearningSUTEJAS
This presentation explores the concept of inductive bias in machine learning. It explains how algorithms come with built-in assumptions and preferences that guide the learning process. You'll learn about the different types of inductive bias and how they can impact the performance and generalizability of machine learning models.
The presentation also covers the positive and negative aspects of inductive bias, along with strategies for mitigating potential drawbacks. We'll explore examples of how bias manifests in algorithms like neural networks and decision trees.
By understanding inductive bias, you can gain valuable insights into how machine learning models work and make informed decisions when building and deploying them.
DEEP LEARNING FOR SMART GRID INTRUSION DETECTION: A HYBRID CNN-LSTM-BASED MODELgerogepatton
As digital technology becomes more deeply embedded in power systems, protecting the communication
networks of Smart Grids (SG) has emerged as a critical concern. Distributed Network Protocol 3 (DNP3)
represents a multi-tiered application layer protocol extensively utilized in Supervisory Control and Data
Acquisition (SCADA)-based smart grids to facilitate real-time data gathering and control functionalities.
Robust Intrusion Detection Systems (IDS) are necessary for early threat detection and mitigation because
of the interconnection of these networks, which makes them vulnerable to a variety of cyberattacks. To
solve this issue, this paper develops a hybrid Deep Learning (DL) model specifically designed for intrusion
detection in smart grids. The proposed approach is a combination of the Convolutional Neural Network
(CNN) and the Long-Short-Term Memory algorithms (LSTM). We employed a recent intrusion detection
dataset (DNP3), which focuses on unauthorized commands and Denial of Service (DoS) cyberattacks, to
train and test our model. The results of our experiments show that our CNN-LSTM method is much better
at finding smart grid intrusions than other deep learning algorithms used for classification. In addition,
our proposed approach improves accuracy, precision, recall, and F1 score, achieving a high detection
accuracy rate of 99.50%.
Presentation of IEEE Slovenia CIS (Computational Intelligence Society) Chapte...University of Maribor
Slides from talk presenting:
Aleš Zamuda: Presentation of IEEE Slovenia CIS (Computational Intelligence Society) Chapter and Networking.
Presentation at IcETRAN 2024 session:
"Inter-Society Networking Panel GRSS/MTT-S/CIS
Panel Session: Promoting Connection and Cooperation"
IEEE Slovenia GRSS
IEEE Serbia and Montenegro MTT-S
IEEE Slovenia CIS
11TH INTERNATIONAL CONFERENCE ON ELECTRICAL, ELECTRONIC AND COMPUTING ENGINEERING
3-6 June 2024, Niš, Serbia
5214-1693458878915-Unit 6 2023 to 2024 academic year assignment (AutoRecovere...
FLUID MECHANICS
1. 1
ASIA PACIFIC UNIVERSITY OF
TECHNOLOGY & INNOVATION
EE0383.5-3-FLM
LAB REPORT FLUID MECHANICS
TITLE LAB REPORT FLUID MECHANICS
NAME & STUDENT ID
MAHMOOD ABDULJABBAR HEBAH
LECTURER LOW YEE SAN
2. 2
ACKNOWLEDGEMENT
“The completion of this undertaking couldn’t have been possible without the
instruction and continues guidance from lecturer Mr. LOW YEE. His contribution is
sincerely appreciated and gratefully acknowledged. As well as my fellow classmates
their useful Participation.”
4. 4
List of Figures
Figure 1 Types of flow...............................................................................................................6
Figure 2 Types of fittings...........................................................................................................7
Figure 3 Internal surface of smooth and rough pipes ................................................................8
Figure 4 Flow shape...................................................................................................................8
Figure 5 Reynold number vs friction coefficient.....................................................................10
Figure 6 Figure 2 : Reynolds Number (Re) .............................................................................11
Figure 7 Sample of head loss ...................................................................................................12
Figure 8 Head Loss. .................................................................................................................12
Figure 9 (K) Geometry Factor. ................................................................................................12
Figure 10 Connection Of The Pipe System .............................................................................13
Figure 11 Setting the Pipe Diameter........................................................................................13
Figure 12 Turn on inlet valve...................................................................................................13
Figure 13 Turn on inlet valve...................................................................................................14
Figure 14 Change manometer knot fro isolate to airvent ........................................................14
Figure 15 Pipe Diameter and Friction Factor Graph ...............................................................16
Figure 16 Head Loss ................................................................................................................16
Figure 17 Time taken to fill up 10cm tank ..............................................................................16
Figure 18 Parameter and calculation by Virtual lab ................................................................17
Figure 19 Parameter and Calculation by Virtual Lab ..............................................................19
5. 5
ABSTRACT
“Begin with the results from 25 mm pipe clearly observed from 3 trials that one
of it are well off the head loss range compared to other trials. As shown in Table 1, for
the 2nd and 3rd trials the head loss is 135.45cm and friction factor 0.026 and the average
friction factor is 0.03. This might be human error or an instrumental error as this was
done by virtual lab. Next, friction factor remained within 0. 001 to 0. 011 in all the three
trials whereas the average was 0.01. Furthermore, as it comes to head loss the pipe had
3 different readings which was between 119.7 to 81.9 cm. End of the experiment, its
proven that Reynold number, Re is more than 4000 and friction factor esteem gives an
implying that the stream is hydraulically smooth. Experiment was effectively
accomplished utilizing virtual lab. As for the calculation part, pipe diameter of 25mm
and 15mm which were tested are compared. As it is noticed, as the velocity of the fluid
flow increases, the head loss increases. Besides, the friction factor increases as the pipe
diameter increases. In conclusion, using velocity which has related to flow rate to
compare the relationship with friction factor, which when the flow rate increase,
velocity of the fluid increase, the friction factor is decreases.”
6. 6
Introduction
“As the significance of fluid mechanics is known in our every day lives. Since
it has boundless applications to automobiles, airplane, and spacecraft, for example,
microscopic biological system. Physical science which manages both fixed and moving
bodies affected by force is fluid mechanics. The consistent domain in fluid mechanics
doesn't hold explicit calculation as in various applications, with position and time the
density of liquid fluctuates. Moreover, mechanical and kinematics conduct of material
in the fluid mechanics is a bit determined mechanics because its displayed as a
consistent mass rather than discrete particles.”
“When fluid flow through pipes, pressure loss (friction) occurs in pipes stream
or passage of pipes. This is because of the impact of liquid consistency of pipes or duct
surface. There are two types of liquid stream turbulent flow and laminar flow.The flow
of water in very smoothly and noticeable is laminar flow whereas turbulent flow, where
the water flows spontaneously, causing it impossible to predict the flow surrounding it.
Turbulent flow can impact the pipes which cause vibration and it will lead in failure.
Furthermore, to identify the type of flow, Reynolds number must be known. Reynold
number predicts the stream design in various fluid flow circumstances, the following
mathematical expression shows if:”
“Turbulent Flow, Re > 4000”
“Transitional Flow, 2300 < Re < 4000”
“Laminar Flow, Re < 2300”
“Usually Re > 4000 for flow in most piping systems”
Figure 1 Types of flow
7. 7
Theory.
“When a gas or a liquid flow through a pipe, the flow of fluid through a pipe is
resisted by viscous shear stresses within the fluid and the turbulence that occurs along
the internal pipe wall. Due to this there will be a loss of pressure in the fluid, because
energy is required to overcome the viscous or frictional forces exerted by the walls of
the pipe on the moving fluid. In addition to the energy lost due to frictional forces, there
will be a loss in energy when the fluid flows through fittings, such as valves, elbows,
contractions and expansions. This loss in pressure is mainly due to the local flow
separation as it moves through such fittings. The pressure loss in pipe flows is
commonly referred to as head loss. The frictional losses are mainly caused in a straight
pipe, friction loss induced in fittings, such as bends, couplings, valves, or transitions in
hose or pipe accounts for minor losses. The frictional losses are referred to as major
losses (hf) while losses through fittings, etc, are called minor losses (hm). Together they
make up the total head losses (h) for pipe flows.”
Figure 2 Types of fittings
“In practice, loss in a pipe flow comes into picture in cases like calculation of
rate of flow in the pipes connecting two reservoirs at different levels or to calculate the
additional head required to double the rate of flow along an existing pipeline. These
pipe losses are dependent on number of factors like viscosity of the fluid, the size of
the internal pipe diameter, the internal roughness of the inner surface of the pipe, the
8. 8
change in elevation between the ends of the pipe, material of the pipe and the length of
the pipe along which the fluid travels.”
“Pipes with smooth surface does not account for larger friction loss, whereas
pipes with less smooth walls such as concrete, cast iron and steel fluid requires large
energy to overcome the friction induced in a pipe due to the viscosity of liquid. Rougher
the inner wall of the pipe, more will be the pressure loss due to friction.”
Figure 3 Internal surface of smooth and rough pipes
Figure 4 Flow shape
(Source: Haung et al 2013)
9. 9
Friction loss in pipe
“The friction loss in a uniform, straight sections of pipe, known as "major loss",
is caused by the effects of viscosity, the movement of fluid molecules against each other
or against the (possibly rough) wall of the pipe. Here, it is greatly affected by whether
the flow is laminar or turbulent. Laminar Flow: It occurs when the fluid flows in parallel
layers without adjacent mixing between the layers. In this type of flow there are neither
eddies nor cross currents, with fast flow over the centre part of the pipe and no
movement near the pipe surface. The roughness of the pipe surface influences neither
the fluid flow nor the friction loss. For laminar flow Reynoldsâ €™s number (Re) <
2100.”
“Turbulent Flow, it occurs when the liquid is moving fast with mixing between
layers. The speed of the fluid at a point continuously undergoes changes in both
magnitude and direction. For turbulent flow Reynolds's number 2100 < Re < 4000”
“Transitional flow: is a mixture of laminar and turbulent flow, with turbulence
flow in the centre of the pipe and laminar flow near the edges of the pipe. Each of these
flows behaves in different manners in terms of their frictional energy loss while flowing
and have different equations that predict their behaviour. For transitional flow
Reynolds's number Re > 4000.”
“It is useful to characterize that roughness as the ratio of the roughness height k
to the pipe diameter D, the relative roughness. Three sub-domains pertain to turbulent
flow:”
“In the smooth pipe domain, friction loss is relatively insensitive to
roughness.”
“In the rough pipe domain, friction loss is dominated by the relative
roughness and is insensitive to Reynolds number.”
“In the transition domain, friction loss is sensitive to both.”
“The Darcy Equation is a theoretical equation that predicts the frictional energy
loss in a pipe based on the velocity of the fluid and the resistance due to friction. It is
used almost exclusively to calculate head loss due to friction in turbulent flow.”
10. 10
“Where:”
“hf = Friction head loss”
“f = Darcy resistance factor”
“L = Length of the pipe”
“D = Pipe diameter”
“v = Mean velocity”
“g = acceleration due to gravity”
“In turbulent flow, the friction factor, f depends upon the Reynolds number and
on the relative roughness of the pipe, k/D, where, k is the roughness parameter and D
is the inner diameter of the pipe. When k is very small compared to the pipe diameter
D i.e., k/D > 0, f depends only on Re. When k/D is a significant value, at low Re, the
flow can be considered as in smooth regime (no effect of roughness). As Re increases,
the flow becomes transitionally rough, called as transition regime in which the friction
factor rises above the smooth value and is a function of both k and Re and Re increases
more and more the flow eventually reaches a fully rough regime in which f is
independent of Re. For design purposes, the frictional characteristics of round pipes,
both smooth and rough are summarized by the friction factor chart, which is a log-log
of fanning friction factor vs Re which is based on Moody's chart.”
Figure 5 Reynold number vs friction coefficient
11. 11
“V = Flow Velocity”
“D = Length of the fluid”
“ρ = Fluid density (
𝑘𝑔
𝑚2 )”
“μ = Dynamic viscosity (Pa s)”
“V = Kinematic viscosity
𝑚2
𝑠
=
𝜇
𝜌
”
Figure 6 Figure 2 : Reynolds Number (Re)
“Friction losses in pipes consider as a complex system geometry in the flow
capacity and the fluid properties of the system. By looking into the mathematical
equation of the square of the flow rate proportional to the head loss. This expression
will lead to the Darcy equation which will allow us to understand many things for the
loss due to friction in pipes. The Darcy equation as shown:”
“APL major loss = Friction pressure loss in fluid flow (Pa(N/m2), psf (lb/ft2).”
“ƒ = Darcy Weisbach friction coefficient”
“L = Length oƒ pipe (m)”
“ρ = Velocity ƒluid (m /s)”
“D = Hydraulic diameter (m, ƒt)”
“V = Fluid density ( kg/m3)”
12. 12
Figure 7 Sample of head loss
“Using this following equation head loss can be identified:”
“Shows fluid statics AP = pgh”
“Thus, h =
𝛥𝑝
𝜌
, Head Loss= f
𝐿
𝐷
𝑉𝑎𝑣𝑔2
2𝑔
”
“One of most broad connections in fluid mechanics is the connection between
pressure loss and head loss and its significant for turbulent or laminar streams, round
or non - circular channels, rough or smooth surface pipes.”
Figure 8 Head Loss.
“Therefore, in laminar flow, relationship between the speed and head loss is
relative as opposed to speed square. Friction factor is in this way contrarily relative to
speed.”
Figure 9 (K) Geometry Factor.
13. 13
Objective
“To determine the friction in the pipe of various diameters.”
Procedures
“A virtual laboratory was utilized for this experiment.”
“As shown in figure 6, five pipes available, and each pipes has an alternate
diameter associated with a stopwatch, differential manometer, an assortment tank,
and scale.”
Figure 10 Connection Of The Pipe System
1.“The 25mm diameter pipe has been chosen for the 1st trial as shown below:”
Figure 11 Setting the Pipe Diameter
2.“All pipes are turned off whereas chosen diameter of pipe is turned on which is 25mm
demonstrated down:”
Figure 12 Turn on inlet valve
14. 14
3.“To flow the water through 25mm chosen pipe, the main inlet valve turned on.”
Figure 13 Turn on inlet valve
4.“When its steady flow in the pipe, change the knot to read the exact position. Turn on
the leeave estimation of collection tank to permit watar streaming in the pipe to
persistently stream outside which shown in figure below:”
Figure 14 Change manometer knot fro isolate to airvent
5.“Manometer perusing has been recorded.”
6.“This been rehashed for 3 trials, at that point followed by different measurements of
the pipe.”
15. 15
Analysis & Results
“The experiment conducted in total of 15 times. To get the average values, three
separated trials performed for each of the five pipes. Table 1shows the values of all
trials obtain from the virtual lab.”
“Table 1: Results from 3 Trials”
“As it shows that friction factor decreases, when the diameter of the pipe
decreases. Therefore, chart underneath shows connection between friction factor and
diameter of the pipe.”
16. 16
Figure 15 Pipe Diameter and Friction Factor Graph
“Manometer displays the readings in trial 2, once set pipes diameter.”
Figure 16 Head Loss
“Head loss was determined by appling following formula since the left limb
reading (LL) is 24.25cm and right limb reading (RL) is 34cm of the manometer.”
“Head Loss (H) = 12.6(left limb — right limb)”
“Head Loss (H) = 12.6 (24.25 – 34)”
“Head Loss (H) = 12.6( -9.75 cm)”
“Head Loss (H) = - 122.85cm”
“Since there is no negative (-) head loss,”
“Head Loss (H) = 122.85cm”
“Time is noted when the exit valve is closed and shown below time taken to fill 10cm tank:”
Figure 17 Time taken to fill up 10cm tank
18. 18
Theoretical calculation
“To obtain the average friction factor by the three trials conducted during the
experiment. Accordingly, 1 trial was taken for calculation and 2 diameters will be
calculated for the pipe.”
“Firstly, the values are set in simulation for diameter 25mm and pipe
length,3m. Thus,”
“Reynold Number (Re) =
𝜌VL
𝜇
”
“Velocity of water (ρ) = 1000”
“Valocity (V) = 279.66 (cm/sec)”
“μ. = (8.9 × 10−4
)”
“Length (L) which is pipe diameter = 25 mm”
“Thus,”
“Reynold Number (Re) =
1000×279.6610−2
×2510−3
8.910−4 ”
“Reynold Number, Re = 78. 556 K”
“To figure friction factor, as demonstrated below Darcy equation used. Thus, the
roughness material (s) to be 0.045mm supposed.”
“ƒ = 0.0255.”
“Consequently, head loss determined as follows:”
“HL = 121.978 cm”
“Percentage of error formula shown below. Simulated values and calculated values are
compared. Table 2:”
“ERROR % =
Simulated Value — Calculated Value
Calculated Value
× 100”
19. 19
“Next, the diameter of pipe is set to 15mm and length same as 3m.”
Figure 19 Parameter and Calculation by Virtual Lab
“Thus,”
“Reynold Number (Re) =
𝜌VL
𝜇
”
“Reynold Number (Re) =
1000×360.2908×10−2
×15×10−3
8.9×10−4 ”
“Reynold Number, Re = 60.723 K”
“To figure friction factor, Darcy equation is utilized as demonstrated below.”
“Thus, the roughness material (s) 0.0001mm supposed.”
“f = 0 .01”
“Head loss determined:”
“HL = 132.32 cm”
20. 20
Discussion
“Based on the result of the experiment, there are many things that can be
discussed regards to the data observed. Beginning to explain about the experiment
conducted through the virtual lab, there are 5 pipes with various diameters to set for
water flow. In this experiment, each pipe has performed 3 trials to get an average
friction factor. The relationship between the head loss and the velocity has been shown
in figure 9, which when the flow rate increases, the velocity of the fluid increase, the
head loss increases. The friction factor is proportional to the pipe diameter. Which
velocity is related to the flow rate from the equation:”
Q =
V
𝑡
“Where,”
“Q = Flow rate”
“V = Velocity”
“T = Time.”
“Begin with the results from 25 mm pipe clearly observed from 3 trials that one
of it are well off the head loss range compared to other trials. As shown in Table 1, for
the 2nd and 3rd trials the head loss is 135.45cm and friction factor 0.026 and the average
friction factor is 0.03. This might be human error or an instrumental error as this was
done by virtual lab.”
“Next, friction factor remained within 0. 001 to 0. 011 in all the three trials
whereas the average was 0.01. Furthermore, as it comes to head loss the pipe had 3
different readings which was between 119.7 to 81.9 cm. End of the experiment, its
proven that Reynold number, Re is more than 4000 and friction factor esteem gives an
implying that the stream is hydraulically smooth. This can be effectively seen by
observing Moody's chart below:”
21. 21
Conclusion
“Experiment was effectively accomplished utilizing virtual lab. As for the
calculation part, pipe diameter of 25mm and 15mm which were tested are compared.
As it is noticed, as the velocity of the fluid flow increases, the head loss increases.
Besides, the friction factor increases as the pipe diameter increases. In conclusion, using
velocity which has related to flow rate to compare the relationship with friction factor,
which when the flow rate increase, velocity of the fluid increase, the friction factor is
decreases.”
22. 22
REFERENCES
P.N Modi and S.M.Seth, “Hydraulics and Fluid Mechanics�,
Standard Book House, Delhi, 2010.
Miller, R. W., Flow Measurement Engineering Handbook, Second Edition,
McGraw-Hill, 1989.
Madan Mohan Das, Fluid Mechanics and Turbo Machines, PHI Learning
Pvt. Ltd, 2008.