The document discusses head loss in pipes due to friction and provides calculations using Darcy's and Chezy's formulas. It then describes two examples: (1) Calculating head loss in a 300mm diameter pipe that is 50m long with water flowing at 3m/s. (2) Finding the diameter of a pipe 2000m long with a flow rate of 200L/s and head loss of 4m using Chezy's formula with C=50. It also summarizes major energy losses from friction and minor losses from expansions, contractions, bends, and fittings.
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.
This document discusses soil mechanics and properties. It covers the origin and classification of soils, particle size distribution, indices like void ratio and specific gravity. Engineering properties like permeability, compressibility and shear strength are also mentioned. Different tests for soil classification like sieve analysis, hydrometer analysis, and Atterberg limits are described. Concepts of three phase diagrams, void ratio, porosity, degree of saturation and their relationships are explained. Engineering applications of void ratio are provided.
This document summarizes the liquid limit and plastic limit tests conducted on a soil sample. The liquid limit was found to be 51.679% using two different methods that produced similar results. The plastic limit was 24.525%. Based on these Atterberg limits, the soil was classified as clay with high plasticity. The limits help characterize the soil's engineering properties and behavior when wet or dry. The experiment showed the soil behaves plastically when wet and becomes hard when dry, typical of clays.
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.
This document provides an overview of laboratory and field testing methods for rocks. It discusses index property tests such as unit weight, porosity, permeability, electrical resistivity, and sonic velocity that are used to characterize and classify rocks. It also describes mechanical property tests like unconfined compressive strength testing, triaxial testing, point load strength testing, and beam bending tests. Common field testing methods mentioned include pressuremeter testing, in-situ direct shear testing, and hydraulic fracturing. The document provides details on sample preparation, equipment used, procedures, and how to calculate and interpret results for different rock property tests.
RMR, or Rock Mass Rating, is a method used to design support plans for underground mine workings based on characteristics of the rock mass. It involves assigning ratings for 5 parameters - layer thickness, structural features, weatherability, rock strength, and groundwater - to determine an overall RMR value. This value is then used to classify the roof rock, estimate expected rock loads, determine the required support resistance and number of roof bolts, and calculate support load density and theoretical strata convergence. The document provides examples of how RMR is applied to these design aspects at a depth of 300m for a mine in India.
This document discusses soil permeability. It defines permeability as the property of a porous material that allows water to pass through its voids. Permeability depends on factors like particle size, void ratio, and degree of saturation. Darcy's law states that the rate of water flow through a soil is proportional to the hydraulic gradient. Common laboratory tests to measure permeability include constant-head and variable-head tests. Permeability is important for calculating seepage, drainage, settlement, and the stability of earth structures. Soils can be classified based on their permeability rate.
This document discusses fluid mechanics concepts related to flow past immersed bodies. It provides examples of fluids flowing over stationary bodies or bodies moving through fluids, such as air over buildings or ships moving through water. It then presents 3 problems involving calculating forces on flat plates moving through air at different velocities based on given coefficients of drag and lift. The document concludes by defining key terms in fluid mechanics such as boundary layer thickness, displacement thickness, and drag force. It also presents 4 additional practice problems calculating forces on objects like parachutes in air based on given properties.
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.
This document discusses soil mechanics and properties. It covers the origin and classification of soils, particle size distribution, indices like void ratio and specific gravity. Engineering properties like permeability, compressibility and shear strength are also mentioned. Different tests for soil classification like sieve analysis, hydrometer analysis, and Atterberg limits are described. Concepts of three phase diagrams, void ratio, porosity, degree of saturation and their relationships are explained. Engineering applications of void ratio are provided.
This document summarizes the liquid limit and plastic limit tests conducted on a soil sample. The liquid limit was found to be 51.679% using two different methods that produced similar results. The plastic limit was 24.525%. Based on these Atterberg limits, the soil was classified as clay with high plasticity. The limits help characterize the soil's engineering properties and behavior when wet or dry. The experiment showed the soil behaves plastically when wet and becomes hard when dry, typical of clays.
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.
This document provides an overview of laboratory and field testing methods for rocks. It discusses index property tests such as unit weight, porosity, permeability, electrical resistivity, and sonic velocity that are used to characterize and classify rocks. It also describes mechanical property tests like unconfined compressive strength testing, triaxial testing, point load strength testing, and beam bending tests. Common field testing methods mentioned include pressuremeter testing, in-situ direct shear testing, and hydraulic fracturing. The document provides details on sample preparation, equipment used, procedures, and how to calculate and interpret results for different rock property tests.
RMR, or Rock Mass Rating, is a method used to design support plans for underground mine workings based on characteristics of the rock mass. It involves assigning ratings for 5 parameters - layer thickness, structural features, weatherability, rock strength, and groundwater - to determine an overall RMR value. This value is then used to classify the roof rock, estimate expected rock loads, determine the required support resistance and number of roof bolts, and calculate support load density and theoretical strata convergence. The document provides examples of how RMR is applied to these design aspects at a depth of 300m for a mine in India.
This document discusses soil permeability. It defines permeability as the property of a porous material that allows water to pass through its voids. Permeability depends on factors like particle size, void ratio, and degree of saturation. Darcy's law states that the rate of water flow through a soil is proportional to the hydraulic gradient. Common laboratory tests to measure permeability include constant-head and variable-head tests. Permeability is important for calculating seepage, drainage, settlement, and the stability of earth structures. Soils can be classified based on their permeability rate.
This document discusses fluid mechanics concepts related to flow past immersed bodies. It provides examples of fluids flowing over stationary bodies or bodies moving through fluids, such as air over buildings or ships moving through water. It then presents 3 problems involving calculating forces on flat plates moving through air at different velocities based on given coefficients of drag and lift. The document concludes by defining key terms in fluid mechanics such as boundary layer thickness, displacement thickness, and drag force. It also presents 4 additional practice problems calculating forces on objects like parachutes in air based on given properties.
This document discusses slope stability and different types of slope failures including translational and rotational. It describes factors that affect slope stability such as erosion, water seepage, earthquakes, and gravity. Methods for analyzing slope stability are presented, including infinite slope analysis, Culmann's method, friction circle method, method of slices, Bishop's method, and Spencer's method. The key parameters in analyzing slope stability are the factor of safety and stability number.
The bulk modulus measures a substance's resistance to uniform compression and is defined as the pressure increase needed to cause a given relative decrease in volume. It has a base unit of Pascal. For example, reducing an iron cannon ball's volume by 0.5% requires increasing the pressure by 0.8 GPa if the bulk modulus is 160 GPa. The bulk modulus is larger for solids than liquids and largest for gases, making solids the least compressible and gases the most compressible.
Effect of underground tunnelling by (TBM) on foundations of existing structuresKishor Ade
This document discusses a dissertation on the effect of underground tunnelling by tunnel boring machine (TBM) on existing structures' foundations. It introduces the topic, provides a literature review on previous related studies, and outlines the methodology, which involves finite element modeling and analysis of shallow and raft foundations at different tunnel depths using Midas GTS NX software. The results found that tunnelling was suitable for raft and shallow foundations on hard and soft murrum soils when the tunnel crown depth was 20-25m below foundations, as displacements did not exceed code limits. Tunnelling was not suitable under shadu soil foundations.
This document discusses Castigliano's theorems for analyzing stresses and strains in structures. It explains that Castigliano's first theorem states that the partial derivative of a structure's strain energy with respect to an applied force equals the displacement at the point of application of that force. Castigliano's second theorem states that the partial derivative of strain energy with respect to a displacement equals the force that produces that displacement. The document provides mathematical expressions to calculate strain energy and uses these theorems to analyze beam deflections under applied loads.
The unconfined compression test is a type of unconsolidated-undrained test used for clay specimens. It involves compressing a cylindrical clay sample axially without lateral confinement. The major principal stress is the axial stress, while the minor principal stresses are zero. This allows measuring the unconfined compressive strength, sensitivity, shear strength parameters, and cohesion of cohesive soils. The test procedure involves extruding and trimming a soil specimen, measuring it, and compressing it at a controlled strain rate between loading plates while recording the load and stress. Parameters are calculated based on the failure load and specimen dimensions.
The document discusses performance of concrete blended with steel fibers. It aims to increase the compressive strength, tensile strength and ductility of concrete. It describes factors affecting the workability of concrete such as water content, mix proportions, size and shape of aggregates, grading of aggregates, and use of admixtures. It also discusses tests to measure workability including slump test and compaction factor test. Compressive strength testing of hardened concrete is also covered.
The document discusses slope stability and factors that influence it. It defines an unrestrained slope and describes different types of slope failures such as base failures and midpoint circle failures. Factors that influence slope stability include soil/rock strength, groundwater, external loading, and slope geometry. Slope failures can be triggered by erosion, rainfall, earthquakes, and construction activities. Methods to improve slope stability include flattening slopes, adding weight/retaining walls, lowering the water table, soil improvement. Stability analyses procedures include mass and slices methods. The factor of safety is defined and equations for infinite slope analysis with and without seepage are provided.
The document provides details on calculating earthwork volumes and costs for a road construction project based on a mass haul diagram (MHD). Key information from the MHD includes:
- Freehaul distance of 600m and balance line at 400 cubic meters
- Freehaul volume of 1500 cubic meters over 600m for a cost of RM9000
- Haul volume of 3075 cubic meters over 610m (average haul distance) for a cost of RM18,757.50
- Overhaul volume of 1575 cubic meters over 750m (average overhaul distance) for a cost of RM2362.50
Total estimated cost of earthwork is RM176,375.
Types of samplers used in soil samplingAna Debbarma
There are two types of soil samples:
1. Disturbed samples - The natural structure of the soil is modified or destroyed during sampling.
2. Undisturbed samples - The natural structure and properties of the soil remain preserved.
Soil sampling devices include open drive samplers, piston samplers, and rotary samplers. Open drive samplers use thin-walled tubes that are pushed into the soil to collect undisturbed samples. Piston samplers also use thin-walled tubes but have a piston inside to prevent excess soil from entering and maintain sample integrity. Rotary samplers have an outer rotating barrel and inner stationary tube to collect annular ring samples.
The document discusses laboratory soil compaction tests. It defines compaction as increasing the bulk density of soil by removing air through external compactive effort. An optimum water content exists where soil achieves maximum density. The document outlines standard and modified Proctor compaction tests and describes how to conduct the tests by compacting soil in layers using specified hammers and measuring dry density at different water contents. Compaction increases soil strength, stability and resistance to erosion while decreasing permeability and compressibility.
Three key phases exist in soil - solids, water, and air. Soil can be saturated (containing water and solids), unsaturated (containing water, air and solids), or dry (containing air and solids only). Parameters such as void ratio, porosity, degree of saturation, water content, and unit weights describe the relative proportions of phases in a soil mass or sample. Phase relationships allow calculation of properties based on the definitions of these parameters.
Alighnment & horizontal alignment of highway (transportation engineering)Civil Zone
This document discusses the alignment of highways, including horizontal and vertical elements. It covers topics such as grade line, horizontal and vertical curves, sight distance requirements, and super elevation. The key points are:
- Highway alignment consists of horizontal and vertical elements, including tangents and curves. Curves can be simple, compound, spiral, or reverse.
- Grade line refers to the longitudinal slope/rise of the highway. Factors in selecting a grade line include earthwork, terrain, sight distance, flood levels, and groundwater.
- Horizontal alignment deals with tangents and circular curves that connect changes in direction. Vertical alignment includes highway grades and parabolic curves.
- Proper design of curves
This presentation is of Penetration Test for Bitumen. Penetration test measures the hardness or softness of bitumen by measuring the depth in tenths of a millimeter to which a standard loaded needle will penetrate vertically in 5 seconds.
There are different grades of Bitumen used for the civil (especially for roads works) work. This presentation consists of the aim, significance, about the apparatus used procedure, noting the reading, Bis recommendation values and IRC recommendation values, precautions,
This document discusses soil classification systems. It begins by describing methods for identifying coarse-grained soils like sand and gravel based on grain size, and fine-grained soils like silt and clay based on properties like dry strength, plasticity, and dispersion testing. It then outlines several soil classification systems including descriptive classification based on particle types, the textural classification triangle, and the Unified Soil Classification System (USCS) which divides soils into coarse-grained, fine-grained, and organic categories based on properties like plasticity and grain size. The USCS is explained in detail through tables. Practical implications of classification systems are that they allow engineers to understand soil behavior based on simple tests and choose suitable sites
The document describes the Indian Standard (IS) Classification System for soils. It divides soils into 3 main categories - coarse grained, fine grained, and highly organic soils - based on grain size. Coarse grained soils are further divided into gravel and sand, each with subcategories based on fines content and plasticity. Fine grained soils are subdivided into low, intermediate, and high compressibility categories based on liquid limit and plasticity index. The document provides detailed explanations of each soil group and examples of classifying soils according to their properties.
Rock Mass Classification and also a brief description of Rock Mass Rating (RMR), Rock Structure Rating (RSR), Q valves and New Austrian Tunneling method(NATM)
This document contains 5 questions regarding fluid mechanics. Question 1 involves calculating the torque and power required to overcome viscous resistance in a rotating shaft. Question 2 involves calculating pressure drop, head loss, and power required for a given water flow rate through a pipe and orifice system. Question 3 determines the necessary counterweight to balance a water gate. Question 4 calculates the water level in a tank given pump specifications and a triangular weir. Question 5 determines if a hydraulic machine is a pump or turbine and calculates its power output or input.
1. The document contains solutions to 10 physics problems involving fluid flow and pressure. Problems involve calculating flow rates, speeds, and pressures using equations like continuity, Bernoulli's principle, and relationships between pressure, density, and height.
2. Key calculations include determining the speed of water flowing over Niagara Falls, the velocity of water through a changing diameter pipe, and the pressure difference between a giraffe's heart and brain due to its height.
3. Questions are solved by setting up and manipulating the relevant equations to find the unknown values, like using continuity to relate velocities at different pipe diameters.
This document discusses slope stability and different types of slope failures including translational and rotational. It describes factors that affect slope stability such as erosion, water seepage, earthquakes, and gravity. Methods for analyzing slope stability are presented, including infinite slope analysis, Culmann's method, friction circle method, method of slices, Bishop's method, and Spencer's method. The key parameters in analyzing slope stability are the factor of safety and stability number.
The bulk modulus measures a substance's resistance to uniform compression and is defined as the pressure increase needed to cause a given relative decrease in volume. It has a base unit of Pascal. For example, reducing an iron cannon ball's volume by 0.5% requires increasing the pressure by 0.8 GPa if the bulk modulus is 160 GPa. The bulk modulus is larger for solids than liquids and largest for gases, making solids the least compressible and gases the most compressible.
Effect of underground tunnelling by (TBM) on foundations of existing structuresKishor Ade
This document discusses a dissertation on the effect of underground tunnelling by tunnel boring machine (TBM) on existing structures' foundations. It introduces the topic, provides a literature review on previous related studies, and outlines the methodology, which involves finite element modeling and analysis of shallow and raft foundations at different tunnel depths using Midas GTS NX software. The results found that tunnelling was suitable for raft and shallow foundations on hard and soft murrum soils when the tunnel crown depth was 20-25m below foundations, as displacements did not exceed code limits. Tunnelling was not suitable under shadu soil foundations.
This document discusses Castigliano's theorems for analyzing stresses and strains in structures. It explains that Castigliano's first theorem states that the partial derivative of a structure's strain energy with respect to an applied force equals the displacement at the point of application of that force. Castigliano's second theorem states that the partial derivative of strain energy with respect to a displacement equals the force that produces that displacement. The document provides mathematical expressions to calculate strain energy and uses these theorems to analyze beam deflections under applied loads.
The unconfined compression test is a type of unconsolidated-undrained test used for clay specimens. It involves compressing a cylindrical clay sample axially without lateral confinement. The major principal stress is the axial stress, while the minor principal stresses are zero. This allows measuring the unconfined compressive strength, sensitivity, shear strength parameters, and cohesion of cohesive soils. The test procedure involves extruding and trimming a soil specimen, measuring it, and compressing it at a controlled strain rate between loading plates while recording the load and stress. Parameters are calculated based on the failure load and specimen dimensions.
The document discusses performance of concrete blended with steel fibers. It aims to increase the compressive strength, tensile strength and ductility of concrete. It describes factors affecting the workability of concrete such as water content, mix proportions, size and shape of aggregates, grading of aggregates, and use of admixtures. It also discusses tests to measure workability including slump test and compaction factor test. Compressive strength testing of hardened concrete is also covered.
The document discusses slope stability and factors that influence it. It defines an unrestrained slope and describes different types of slope failures such as base failures and midpoint circle failures. Factors that influence slope stability include soil/rock strength, groundwater, external loading, and slope geometry. Slope failures can be triggered by erosion, rainfall, earthquakes, and construction activities. Methods to improve slope stability include flattening slopes, adding weight/retaining walls, lowering the water table, soil improvement. Stability analyses procedures include mass and slices methods. The factor of safety is defined and equations for infinite slope analysis with and without seepage are provided.
The document provides details on calculating earthwork volumes and costs for a road construction project based on a mass haul diagram (MHD). Key information from the MHD includes:
- Freehaul distance of 600m and balance line at 400 cubic meters
- Freehaul volume of 1500 cubic meters over 600m for a cost of RM9000
- Haul volume of 3075 cubic meters over 610m (average haul distance) for a cost of RM18,757.50
- Overhaul volume of 1575 cubic meters over 750m (average overhaul distance) for a cost of RM2362.50
Total estimated cost of earthwork is RM176,375.
Types of samplers used in soil samplingAna Debbarma
There are two types of soil samples:
1. Disturbed samples - The natural structure of the soil is modified or destroyed during sampling.
2. Undisturbed samples - The natural structure and properties of the soil remain preserved.
Soil sampling devices include open drive samplers, piston samplers, and rotary samplers. Open drive samplers use thin-walled tubes that are pushed into the soil to collect undisturbed samples. Piston samplers also use thin-walled tubes but have a piston inside to prevent excess soil from entering and maintain sample integrity. Rotary samplers have an outer rotating barrel and inner stationary tube to collect annular ring samples.
The document discusses laboratory soil compaction tests. It defines compaction as increasing the bulk density of soil by removing air through external compactive effort. An optimum water content exists where soil achieves maximum density. The document outlines standard and modified Proctor compaction tests and describes how to conduct the tests by compacting soil in layers using specified hammers and measuring dry density at different water contents. Compaction increases soil strength, stability and resistance to erosion while decreasing permeability and compressibility.
Three key phases exist in soil - solids, water, and air. Soil can be saturated (containing water and solids), unsaturated (containing water, air and solids), or dry (containing air and solids only). Parameters such as void ratio, porosity, degree of saturation, water content, and unit weights describe the relative proportions of phases in a soil mass or sample. Phase relationships allow calculation of properties based on the definitions of these parameters.
Alighnment & horizontal alignment of highway (transportation engineering)Civil Zone
This document discusses the alignment of highways, including horizontal and vertical elements. It covers topics such as grade line, horizontal and vertical curves, sight distance requirements, and super elevation. The key points are:
- Highway alignment consists of horizontal and vertical elements, including tangents and curves. Curves can be simple, compound, spiral, or reverse.
- Grade line refers to the longitudinal slope/rise of the highway. Factors in selecting a grade line include earthwork, terrain, sight distance, flood levels, and groundwater.
- Horizontal alignment deals with tangents and circular curves that connect changes in direction. Vertical alignment includes highway grades and parabolic curves.
- Proper design of curves
This presentation is of Penetration Test for Bitumen. Penetration test measures the hardness or softness of bitumen by measuring the depth in tenths of a millimeter to which a standard loaded needle will penetrate vertically in 5 seconds.
There are different grades of Bitumen used for the civil (especially for roads works) work. This presentation consists of the aim, significance, about the apparatus used procedure, noting the reading, Bis recommendation values and IRC recommendation values, precautions,
This document discusses soil classification systems. It begins by describing methods for identifying coarse-grained soils like sand and gravel based on grain size, and fine-grained soils like silt and clay based on properties like dry strength, plasticity, and dispersion testing. It then outlines several soil classification systems including descriptive classification based on particle types, the textural classification triangle, and the Unified Soil Classification System (USCS) which divides soils into coarse-grained, fine-grained, and organic categories based on properties like plasticity and grain size. The USCS is explained in detail through tables. Practical implications of classification systems are that they allow engineers to understand soil behavior based on simple tests and choose suitable sites
The document describes the Indian Standard (IS) Classification System for soils. It divides soils into 3 main categories - coarse grained, fine grained, and highly organic soils - based on grain size. Coarse grained soils are further divided into gravel and sand, each with subcategories based on fines content and plasticity. Fine grained soils are subdivided into low, intermediate, and high compressibility categories based on liquid limit and plasticity index. The document provides detailed explanations of each soil group and examples of classifying soils according to their properties.
Rock Mass Classification and also a brief description of Rock Mass Rating (RMR), Rock Structure Rating (RSR), Q valves and New Austrian Tunneling method(NATM)
This document contains 5 questions regarding fluid mechanics. Question 1 involves calculating the torque and power required to overcome viscous resistance in a rotating shaft. Question 2 involves calculating pressure drop, head loss, and power required for a given water flow rate through a pipe and orifice system. Question 3 determines the necessary counterweight to balance a water gate. Question 4 calculates the water level in a tank given pump specifications and a triangular weir. Question 5 determines if a hydraulic machine is a pump or turbine and calculates its power output or input.
1. The document contains solutions to 10 physics problems involving fluid flow and pressure. Problems involve calculating flow rates, speeds, and pressures using equations like continuity, Bernoulli's principle, and relationships between pressure, density, and height.
2. Key calculations include determining the speed of water flowing over Niagara Falls, the velocity of water through a changing diameter pipe, and the pressure difference between a giraffe's heart and brain due to its height.
3. Questions are solved by setting up and manipulating the relevant equations to find the unknown values, like using continuity to relate velocities at different pipe diameters.
The document contains multiple physics problems involving fluid flow through pipes and tubes. It provides the equations for volume flow rate, velocity, pressure, and other variables related to fluid dynamics. It then asks the reader to use these equations to calculate requested values like velocity, pressure, flow rate, and more at different points in pipes/tubes given conditions like pipe diameter, fluid velocity, pressure, height, and flow rate.
1. The document discusses basic principles of pipe flow, including the continuity equation and equations of motion for steady flow in pipes. It defines terms like pressure head, velocity head, and head loss.
2. It covers topics like surface resistance (friction loss), minor losses from bends/elbows/valves, and form losses from transitions and other components. Equations are provided for calculating friction factor and head losses.
3. Examples are given to demonstrate calculating friction loss in a pipe and flow rates in inclined pipes using the provided equations. Pipe material roughness heights and common form loss coefficients are also tabulated.
This document discusses fluid flow in pipes under pressure. It presents equations to describe laminar and turbulent flow. For laminar flow, the Hagen-Poiseuille equation gives the relationship between pressure drop and flow rate. For turbulent flow, the velocity profile consists of a thin viscous sublayer near the wall and a fully turbulent center zone. Equations are derived to describe velocity profiles in both the sublayer and center zone based on viscosity and turbulence effects. Pipes are classified as smooth or rough depending on roughness size compared to the sublayer thickness.
This document contains solutions to examples related to wave motion. It begins by finding the period and phase speed of a wave given its wavelength or depth, using the dispersion relationship. It then calculates wave properties like height, velocity, energy, and power from pressure sensor readings. Further sections determine wave characteristics in deep water, shallow water, and when a current is present. The document solves for wavelength, period, phase speed and direction in examples involving deep water, shallow water and coastal refraction.
1. The document discusses principles of pipe flow, including siphon action where a pipeline rises above the hydraulic gradient line. It provides equations to calculate head loss due to friction in pipes.
2. An example problem is presented to calculate residual pressure at the end of a pipe outlet for a pumping system with different pipe fittings, applying equations for head loss calculations.
3. Common pipe flow problems like nodal head, discharge, and diameter problems are introduced and equations are provided to solve each type of problem.
The document discusses energy losses in pipeline systems. It covers topics such as velocity profiles in pipes, sources of energy loss including shock losses at enlargements and contractions, friction losses, and examples of calculating losses. Bernoulli's equation is applied to analyze pressure and velocity changes between points along pipelines. Key sources of loss are friction against pipe walls and shocks caused by changes in pipe diameter.
1) The document is a lecture summary from a fluid mechanics course taught by Dr. Bijit Kumar Banik at Shahjalal University of Science and Technology.
2) It covers topics related to impulse-momentum principles, including the momentum correction factor for non-uniform flow, examples of forces on vanes and nozzles, and homework problems from the textbook.
3) Sample problems are worked through, such as determining the magnitude and direction of the resultant force on a double nozzle, and calculating the forces on a stationary vane where the fluid jet velocity is reduced due to friction.
hydraulics and advanced hydraulics solved tutorialsbakhoyaagnes
The document provides solutions to several hydraulic engineering assignments. Assignment 8 asks to find the critical slope and specific energy for a trapezoidal channel given various parameters including a Froude number of 0.12. The solution shows:
1) Using Manning's equation and the given Froude number, relationships are developed between flow rate, depth, and other variables.
2) By iterative solution, the normal flow depth is found to be 0.51m and flow rate 1.132 m3/s.
3) Similarly, the critical depth is found to be 0.125m by setting the Froude number equal to 1.
4) The critical slope is then calculated using the critical flow parameters to
This document provides information about gradually varied flow and rapidly varied flow in hydraulics. It discusses gradually varied flow, including definitions, equations, and classifications of profiles. It also briefly discusses rapidly varied flow and includes formulas and characteristics. The document contains an example problem involving a prismatic channel with three sections of varying slope, a sluice gate, and a horizontal transition. The problem involves determining flow conditions, critical depths, and water surface profiles for each section. The objectives are to analyze the problem, determine if the gate operates under free flow or submerged flow conditions, and calculate maximum transition length and head loss.
1. Bernoulli's equation relates pressure, elevation, and velocity in fluid flow and is used to measure flow velocity in devices like pitot tubes, venturi meters, and orifices.
2. A pitot-static tube connected to a manometer can be used to measure flow velocity by determining the difference between stagnation and static pressures.
3. For an orifice, the actual discharge is less than the theoretical discharge due to losses. The coefficient of discharge accounts for losses and is used to calculate actual flow rate.
1. The document provides answers to example problems involving wave propagation and hydraulics. It analyzes wave characteristics such as wavelength, phase speed, and acceleration for different water depths.
2. Methods like iteration of the dispersion relationship are used to determine wave numbers and properties for scenarios with and without current.
3. Key wave parameters like height and wavelength are calculated from pressure readings using linear wave theory and shoaling equations. Different cases consider deep, intermediate, and shallow water conditions.
Practica física II Estática de fluidosjoseluis1261
The document provides solutions to problems involving fluid statics concepts like pressure, density, and buoyancy. It calculates pressures in different units, the pressure on a submarine at depth, the average pressure on a dam wall, and more. Key calculations involve converting between pressure units, using formulas like pressure = density x gravity x height, and applying concepts such as equal volumes in hydraulic systems.
This document provides design recommendations for an isolated square footing foundation, including:
- The allowable bearing capacity of the soil is 314 kN/m^2 at a minimum depth of 2 meters.
- For a given service load of 1230.3 kN dead load and 210.6 kN live load, the required base area is calculated as 5.18 m^2 and the footing size is determined to be 2.3x2.3 meters.
- The required thickness is determined to be 500 mm based on checks for one-way shear, two-way punching shear, flexure in the long direction, and flexure in the short direction. Steel reinforcement of 12 bars of
The document discusses the Hardy Cross Method for analyzing water distribution systems to determine pressures and flows. It involves the following steps:
1. Assume pipe diameters and initial flows such that the sum of inflows equals outflows at junctions.
2. Calculate head losses in each pipe using the Hazen-Williams equation.
3. Calculate flow corrections using an equation that sets the sum of head losses around loops to zero.
4. Repeat using corrected flows until flow corrections become small.
An example problem applies the method to determine suitable pipe diameters for a branching system given pressure requirements at nodes.
This document provides guidance on designing irrigation systems. It discusses key concepts like water flow in pipes, hydrostatic pressure, pressure head, total head, head loss, and lateral pipe characteristics. The document presents examples of calculating water velocity, flow rate, pipe diameter, and pressure at different points in an irrigation system. It also discusses alternatives for designing manifolds and ensuring even distribution of pressure and water across subplots. The overall aim is to provide practical methods for designing efficient pressure irrigation systems.
This document provides guidance on designing irrigation systems. It discusses key concepts like water flow in pipes, hydrostatic pressure, head loss, and lateral pipe characteristics. The document presents examples calculating water velocity, flow rate, pipe diameter, and pressure under different system configurations. It also examines alternatives for designing manifolds and subplots. The overall aim is to provide practical methods for laying out any pressure irrigation system based on hydraulic principles.
This document discusses open channel hydraulics and specific energy. It defines key terms like head, energy, hydraulic grade line, energy line, critical depth, Froude number, specific energy, and gradually varied flow. It explains the concepts of critical depth, alternate depths, and how specific energy relates to critical depth for rectangular and non-rectangular channels. It also discusses surface profiles, backwater curves, types of bed slopes, occurrence of critical depth with changes in bed slope, and the energy equation for gradually varied flow. An example problem is included to demonstrate calculating distance between depths for gradually varied flow.
This document discusses the calculation of machining time for various operations. It provides formulas and factors to consider for estimating machining time for lathe operations like turning, facing, knurling, reaming, etc. It also discusses machining time calculation for other operations like milling, shaping, planning, drilling, boring, grinding. Key factors that influence machining time include tool travel, feed, depth of cut, rpm, cutting speed, setup time, operation time, tear down time and allowances. Accurate estimation of machining time is important for production costing and manufacturing cost estimation of parts.
This document discusses process planning and cost estimation for various manufacturing processes like forging, welding, and foundry. It provides details on the forging process types like hand forging, drop forging, and press forging. It also describes the steps to estimate the cost of production for each process, including calculating material, labor, and overhead costs. The key cost elements discussed are material selection and allowances for patterns, labor time estimation, and treating overheads as a percentage of labor cost.
This document discusses cost estimation for process planning and manufacturing. It defines cost estimation as predicting production costs before actual manufacturing. The key steps in cost estimation are: 1) Analyzing product requirements and specifications, 2) Preparing a bill of materials, 3) Estimating material, labor, tooling and purchased part costs, 4) Calculating prime cost by adding direct costs, 5) Applying factory overhead costs, 6) Adding administrative and selling expenses to get total cost, and 7) Factoring in profit to determine selling price. Common cost estimation methods include factor method, material cost method, and function method. The document outlines elements of cost like material, labor, overhead and provides examples of cost estimation calculations.
This document discusses topics related to process planning, cost estimation, and quality assurance for manufacturing processes. It covers units on process planning activities, cost estimation techniques like production costing, and machining time calculations. Additionally, it outlines quality assurance methods like the seven basic statistical quality control tools, control charts, and considerations for selecting appropriate measurement instruments based on factors like accuracy, resolution, and sensitivity.
The document discusses the key activities involved in process planning, including drawing interpretation, material and process selection, selection of machines, tools and workholding devices, determining process parameters and quality assurance methods, cost estimation, documentation, and communicating the process plan. It provides details on each step, for example explaining that drawing interpretation provides critical information like materials, dimensions, tolerances. Process selection involves evaluating factors like the part geometry, required material properties, and manufacturability. Machine selection depends on economic and operational considerations. The document also discusses related topics like computer-aided process planning and factors that influence tooling selection.
The document discusses different types of clutches used to connect and disconnect rotating shafts. It describes friction clutches including single plate, multi-plate, and cone clutches. It explains how they work using friction between contacting surfaces. Centrifugal clutches are also discussed which use centrifugal force rather than springs to engage. The key functions of clutches are to connect/disconnect shafts, start/stop machines smoothly, and reduce shocks between shafts.
A transmission provides speed and torque conversions from an engine to another device using gear ratios. This reduces wear on the engine and allows greater control and higher speeds. There are several types of transmissions including manual, epicyclic, and automatic. Manual transmissions include sliding mesh, constant mesh, and synchromesh types. Automatic transmissions include hydromatic and torque converter types. The document discusses characteristics and design considerations for gearboxes.
Bevel gears are used to transmit power between two intersecting shafts at 90 degree angles. There are several types of bevel gears including straight bevel gears which have teeth parallel to the pitch cones, spiral bevel gears which have teeth inclined to the face, and zerol bevel gears which are spiral gears with curved teeth but zero spiral angle. Bevel gears can also be classified based on their pitch angles as mitre gears with perpendicular shafts, angular gears with non-perpendicular shafts, or crown gears where one gear has a 90 degree pitch angle. The design of bevel gears involves calculating the gear ratio and selecting materials, determining the initial torque load, selecting tooth dimensions, and choosing the proper number
The document provides information on spur gears, including definitions, types, classifications, terminology, design procedure, materials, and manufacturing methods. Some key points:
- Spur gears are circular gears with straight teeth used to transmit motion between parallel shafts.
- Gears can be classified based on shaft position, motion type, peripheral speed, tooth position, and gearing type.
- The design procedure involves calculating torque, stresses, module, teeth number, dimensions, and checking safety.
- Common materials include steel, cast iron, and bronze. Selection depends on application factors.
- Gears are manufactured through milling, generating, shaping, molding, and casting processes.
This document discusses the design of transmission systems. It covers various types of belt drives used to transmit power between shafts including flat belts, V-belts, circular belts, and discusses factors to consider when selecting a belt drive such as the power needs, shaft speeds and layout. It also describes types of flat belt drives, materials used for belts, and defines concepts like velocity ratio, slip and creep in belt drives.
The document discusses hydraulic turbines and hydroelectric power plants. It describes how hydraulic turbines convert the kinetic and potential energy of water into mechanical energy using an impulse turbine called a Pelton wheel. The Pelton wheel has buckets that are struck by high-speed jets of water which causes the wheel to spin and power a generator to produce hydroelectricity. The document provides details on the components of a Pelton wheel like the nozzle, runner, and buckets. It also includes diagrams of a typical hydroelectric power plant layout and formulas used in calculating efficiencies and power values.
1. The document discusses pumps, specifically centrifugal pumps. It defines pumps and explains that their purpose is to transfer mechanical energy into pressure or kinetic energy to lift or transfer liquids.
2. Centrifugal pumps are classified based on their mechanical principles. They work by using an impeller to impart centrifugal force on a liquid and increase pressure.
3. The key components of a centrifugal pump are described in detail, including the impeller, casing, suction pipe, strainer, foot valve, and delivery pipe. The document also explains how centrifugal pumps work and the steps involved in their operation.
The document discusses dimensional analysis and its applications. Dimensional analysis is a technique used in research and design to analyze the relationships between different physical quantities. It involves identifying the fundamental and derived quantities involved in a phenomenon and determining their dimensions. Dimensional analysis helps derive dimensionless parameters and homogeneous equations. It aids in testing equations, designing model experiments, and presenting results systematically. The document provides examples of applying dimensional analysis techniques like Rayleigh's and Buckingham π methods to fluid mechanics problems to determine functional relationships between variables.
Unit I discusses fluid properties and flow characteristics. It covers fluid density, viscosity, surface tension, compressibility, and vapor pressure. It also discusses the concepts of control volume and the application of continuity, energy, and momentum equations to fluid flow. Specific topics covered include density, specific gravity, viscosity, surface tension, capillarity, compressibility, and vapor pressure. Several sample problems are worked through to demonstrate calculations for properties like density, specific weight, viscosity, surface tension, and capillary rise.
The document discusses various aspects of planning including defining goals and strategies, types of plans, objectives of planning, the planning process, and management by objectives. It provides details on strategic planning, operational planning, long and short-term planning, setting objectives, the management by objectives approach, and contingency factors to consider in planning.
The document provides an overview of management principles including:
- Defining management as the process of planning, organizing, leading, and controlling organizational resources to efficiently achieve goals.
- Describing the four functions of management as planning, organizing, leading, and controlling.
- Explaining the different levels of management as top-level, middle-level, and lower-level/supervisory management.
This document discusses different types of bearings, including radial bearings which support radial loads, thrust bearings which support axial loads, and journal bearings which include full, partial, and fitted types to support shafts and rotational movement. It also mentions the design of journal bearings.
This document discusses different types of springs and their applications. It provides information on helical springs, leaf springs, disc springs, and helical spring design. The key points are:
- Springs store and release energy through elastic deformation, returning to their original shape after loading. Common applications include automobiles, trains, valves, and watches.
- Helical springs can be open or closed coil and are made of wire coiled into a helix. Leaf springs use stacked flat plates. Disc springs use stacked discs.
- Springs cushion impacts, absorb/store energy, apply/control forces and motions. Helical spring design considers factors like wire diameter, coil diameter, and number of coils.
A knuckle joint connects two rods under tensile loads. It consists of a forked or double eye rod, a single eye rod, and a knuckle pin. The joint allows a small angular movement of one rod relative to the other. Applications include elevator chains and valve rods. It allows rods subjected to tensile and compressive forces to connect and disconnect while accommodating some angular movement.
Couplings are devices used to connect two shafts together to transmit power between machines. There are different types of couplings like flexible couplings, universal couplings, and Oldham's couplings that can connect shafts with some misalignment or adapt to speed changes. The design procedure for couplings involves selecting the appropriate type based on the application requirements and connecting conditions between machine components.
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.
A review on techniques and modelling methodologies used for checking electrom...nooriasukmaningtyas
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Robust Intrusion Detection Systems (IDS) are necessary for early threat detection and mitigation because
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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
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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,
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Cooperation Organisation and the Belt and Road Economic Initiative.
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.
4. Find the head lost due to friction in a pipe of diameter 300 mm and
length 50 m, through which water is flowing at a velocity of 3 m/s
using (i) Darcy formula, (ii) Chezy’s formula for which C = 60.
Given:
D = 300 mm = 0.3 m
L = 50 m
V = 3 m/s
C = 60
𝛾 = 0.01 stoke = 0.01 cm2/s = 0.01 * 10-4 m2/s
To find:
hf
(i) Darcy formula
(ii) Chezy’s Formula
𝛾 𝜋 𝜇 𝜌 2
1
2
5. Darcy Eqn:
hf =
4 𝑓 𝐿 𝑉2
2 𝑔𝑑
Re =
𝑣 𝑑
𝛾
=
3 ∗ 0.3
0.01 ∗ 10−4 = 90 x 104 > 2000
Hence it is Turbulent flow
So, f =
0.079
𝑅𝑒0
.
25 =
0.079
(90 𝑥 104) 0.25
= 2.56 x 10-3
hf =
4 ∗2.56 x 10−3∗50 ∗ 32
2 ∗9.81 ∗0.3
=> hf = 0.7828 m
Chezy’s Eqn
V = C 𝑚𝑖 𝒐𝒓 𝒉𝒇 =
𝟒×𝑳×𝑽𝟐
𝑪𝟐
× 𝒅
V = C
𝑑
4
ℎ𝑓
𝐿
3 = 60
0.3
4
ℎ𝑓
50
hf = 1.665 m
6. Find the diameter of a pipe of length 2000 m when the rate of flow of water
through the pipe is 200 litres/s and the head lost due to friction is 4 m. Take the
value of C = 50 in chezy’s formulae.
Given
L = 2000 m
Q = 200 lit/s = 0.2 m3/s → Q = A V
hf = 4 m
C = 50
To find:
d
Solution:
V = C 𝑚𝑖
7. (or) ℎ𝑓 =
4×𝐿×𝑉2
𝐶2
× 𝑑
ℎ𝑓 =
4 𝑥 2000×𝑉2
𝐶2
× 𝑑
Discharge, Q = A V
0.2 =
𝜋
4
d2 * V
V =
0.8
𝜋 d2
ℎ𝑓 =
4 𝑥 2000×𝑉2
𝐶2
× 𝑑
4 =
4 𝑥 2000×
0.8
𝜋 d2
2
502
× 𝑑
d = 0.553 m = 553 mm
8. Loss of Energy in pipes:
When a fluid is flowing through a pipe, the fluid experiences some resistances due to
which some of the energy of fluid is lost. This loss of energy is classified a
Energy Losses
Major Energy Losses
This is due to friction and its is calculated
by the following formulae:
(a) Darcy – Weisbach Formula
(b) Chezy’s Formula
Minor Energy Losses
This is due to
(a) Sudden expansion of pipe,
(b) Sudden contraction of pipe,
(c) Bend in pipe,
(d) Pipe fittings, etc.,
(e) An obstruction in pipe.
9. MAJOR LOSS
❖ The major loss of energy is due to friction
❖ The loss due to friction is much more in case of long pipe
lines.
❖ It depends on roughness of pipe, length, velocity and
diameter of pipe.
𝒉𝒇 =
𝟒 × 𝒇 × 𝑳 × 𝑽𝟐
𝟐 × 𝒈 × 𝒅
From DARCY’S WEISBACH EQUATION
𝒉𝒇 =
𝟒 × 𝑳 × 𝑽𝟐
𝑪𝟐 × 𝒅
From Chezy′s EQUATION
10. MINOR LOSS
❖ The losses due to disturbance in flow pattern is called
as minor loss
❖ Minor loss occurs due to
❖ Sudden Expansion
❖ Sudden Contraction
❖ Valves
❖ Fittings
❖ Bends
11. LOSS OF ENERGY DUE SUDDEN ENLARGEMENT
❖ Consider a horizonal pipe of
area A1 is suddenly enlarged to
the area A2
𝑷𝟏𝑨𝟏
𝑷𝟐𝑨𝟐
𝑽𝟏 𝑽𝟐
① ②
❖ Consider a two section of ①and
② is before and after
expansion.
❖ Let 𝑷𝟏𝑨𝟏𝒂𝒏𝒅 𝑽𝟏 is the Pressure
Intensity, Velocity at area A1
❖ Let 𝑷𝟐𝑨𝟐𝒂𝒏𝒅 𝑽𝟐is the Pressure Intensity, Velocity at area A2
❖ Let 𝑷′is the intensity of pressure, of the liquid Eddies on Area A2 – A1
12. LOSS OF ENERGY DUE SUDDEN ENLARGEMENT
❖ The resultant force between section ① & ②
𝑭 = 𝑷𝟏𝑨𝟏 − 𝑷𝟐𝑨𝟐 + 𝑷′
(𝑨𝟐 − 𝑨𝟏)
❖ But it has been found by experiment that
𝑷′
= 𝑷𝟏
❖ The resultant force
𝑭 = 𝑷𝟏𝑨𝟏 − 𝑷𝟐𝑨𝟐 + 𝑷𝟏(𝑨𝟐 − 𝑨𝟏)
𝑭 = 𝑷𝟏𝑨𝟏 − 𝑷𝟐𝑨𝟐 + 𝑷𝟏𝑨𝟐 − 𝑷𝟏𝑨𝟏
𝑭 = 𝑷𝟏 − 𝑷𝟐 𝑨𝟐
13. LOSS OF ENERGY DUE SUDDEN ENLARGEMENT
❖ Momentum of liquid / sec at section ①
= 𝑴𝒂𝒔𝒔 × 𝑽𝒆𝒍𝒐𝒄𝒊𝒕𝒚
= 𝝆𝑨𝟏𝑽𝟏 × 𝑽𝟏
= 𝝆𝑨𝟏𝑽𝟏
𝟐
❖ Momentum of liquid / sec at section ②
= 𝝆𝑨𝟐𝑽𝟐 × 𝑽𝟐
= 𝝆𝑨𝟐𝑽𝟐
𝟐
14. LOSS OF ENERGY DUE SUDDEN ENLARGEMENT
❖ Change in Momentum of liquid / sec
= 𝝆𝑨𝟐𝑽𝟐
𝟐
− 𝝆𝑨𝟏𝑽𝟏
𝟐
❖ From Continuity Equation
𝑨𝟏𝑽𝟏 = 𝑨𝟐𝑽𝟐 𝑨𝟏 =
𝑨𝟐𝑽𝟐
𝑽𝟏
= 𝝆𝑨𝟐𝑽𝟐
𝟐
− 𝝆
𝑨𝟐𝑽𝟐
𝑽𝟏
𝑽𝟏
𝟐
= 𝝆𝑨𝟐𝑽𝟐
𝟐
− 𝝆𝑨𝟐𝑽𝟏𝑽𝟐
15. LOSS OF ENERGY DUE SUDDEN ENLARGEMENT
❖ From Newton’s Second Law of motion
𝑭𝒐𝒓𝒄𝒆 = 𝑹𝒂𝒕𝒆 𝒐𝒇 𝒄𝒉𝒂𝒏𝒈𝒆 𝒐𝒇 𝒎𝒐𝒎𝒆𝒏𝒕𝒖𝒎 𝒐𝒇 𝒕𝒉𝒆 𝒎𝒂𝒔𝒔
𝑷𝟏 − 𝑷𝟐 𝑨𝟐 = 𝝆𝑨𝟐𝑽𝟐
𝟐
− 𝝆𝑨𝟐𝑽𝟏𝑽𝟐
𝑷𝟏 − 𝑷𝟐 𝑨𝟐 = 𝝆𝑨𝟐(𝑽𝟐
𝟐
− 𝑽𝟏𝑽𝟐)
𝑷𝟏 − 𝑷𝟐
𝝆
= (𝑽𝟐
𝟐
− 𝑽𝟏𝑽𝟐)
17. LOSS OF ENERGY DUE SUDDEN ENLARGEMENT
𝑽𝟐
𝟐
−𝑽𝟏𝑽𝟐
𝒈
= +
𝑽𝟐
𝟐
𝟐𝒈
+ 𝒛𝟐 −
𝑽𝟏
𝟐
𝟐𝒈
− 𝒛𝟏 + 𝒉𝒆
❖ Datum head of section ① & ② are equal
∴ 𝒛𝟏= 𝒛𝟐
𝑽𝟐
𝟐
−𝑽𝟏𝑽𝟐
𝒈
=
𝑽𝟐
𝟐
𝟐𝒈
−
𝑽𝟏
𝟐
𝟐𝒈
+ 𝒉𝒆 𝒉𝒆 =
𝟐𝑽𝟐
𝟐
−𝟐𝑽𝟏𝑽𝟐−𝑽𝟐
𝟐
−𝑽𝟏
𝟐
𝟐𝒈
𝒉𝒆 =
𝑽𝟐
𝟐
−𝟐𝑽𝟏𝑽𝟐−𝑽𝟏
𝟐
𝟐𝒈
𝒉𝒆 =
𝑽𝟏−𝑽𝟐
𝟐
𝟐𝒈
18. The rate of flow of water through a horizontal pipe is 0.3m3/sec. the diameter of the pipe,
which is 25cm, is suddenly enlarged to 50 cm. the pressure intensity in the smaller pipe is 14
N/cm2. determine the loss of head due to sudden enlargement, pressure intensity in the larger
pipe power lost due to enlargement.
Given
Q = 0.3 m3/sec
D1 = 25 cm = 0.25 m
D2 = 50 cm = 0.5 m
p1 = 14 N/cm2 = 14 * 104 N/m2
To find:
he
p2
P
Solution:
Q = A1 V1 => V1 = Q/A1 = Q/(
𝜋
4
d1
2 ) = 6.11 m/s
Q = A2 V2 => V2 = Q/A2 = Q/(
𝜋
4
d2
2 ) = 1.52 m/s
22. LOSS OF ENERGY DUE SUDDEN CONTRACTION
❖ From Continuity Equation
𝑨𝒄𝑽𝒄 = 𝑨𝟐𝑽𝟐
𝑽𝒄
𝑽𝟐
=
𝑨𝟐
𝑨𝒄
𝑽𝒄
𝑽𝟐
=
𝟏
𝑨𝒄/𝑨𝟐
𝑽𝒄
𝑽𝟐
=
𝟏
𝑪𝒄
23. LOSS OF ENERGY DUE SUDDEN CONTRACTION
𝐡𝐜 =
𝑽𝟐
𝟐
𝟐𝒈
𝟏
𝑪𝒄
− 𝟏
𝟐
𝐡𝐜 =
𝒌𝑽𝟐
𝟐
𝟐𝒈 𝒔𝒊𝒏𝒄𝒆 𝒌 =
𝟏
𝑪𝒄
− 𝟏
𝟐
❖ If the valve of CC is not given, then
𝐡𝐜 =
𝟎.𝟓𝑽𝟐
𝟐
𝟐𝒈
24. In Fig shown below, when a sudden contraction is introduced in a horizontal pipe line from 50 cm to 25
cm, the pressure changes from 10,500 kg/m2 (103005 N/m2) to 6900 kg/m2 (67689 N/m2). Calculate the rate
of flow. Assume co-efficient of contraction of jet to be 0.65. Following this if there is a sudden enlargement
from 25 cm to 50cm and if the pressure at the 25 cm section is 6900 kg/m2 (67689 N/m2) what is the
pressure at the 50 cm enlarged section?
Given:
D1 = 50 cm = 0.5 m
D2 = 25 cm = 0.25 m
p1 = 103005 N/ m2
p2 = 67689 N/ m2
p3 = 67689 N/ m2
CC = 0.65
D4 = 50 cm = 0.5 m
D3= 25 cm = 0.25 m
To find:
Q
p4
27. LOSS OF ENERGY AT ENTRANCE AND EXIT
𝐡𝐢 =
𝟎.𝟓𝑽𝟏
𝟐
𝟐𝒈
❖ Loss of energy at Entrance
❖ Loss of energy at Exit
𝐡𝐨 =
𝑽𝟐
𝟐
𝟐𝒈
28. LOSS OF ENERGY DUE TO GRADUAL CONTRACTION AND EXPANSION
𝐡𝐠 =
𝒌 𝑽𝟏−𝑽𝟐
𝟐
𝟐𝒈
𝐡𝐛 =
𝒌𝑽𝟐
𝟐𝒈
LOSS OF ENERGY DUE TO BEND IN A PIPE
29. LOSS OF ENERGY DUE TO VARIOUS PIPE FITTINGS
𝐡𝐯 =
𝒌𝑽𝟐
𝟐𝒈
𝐡𝐨𝐛 =
𝑽𝟐
𝟐𝒈
𝑨
𝑪𝑪(𝑨−𝒂)
− 𝟏
LOSS OF ENERGY DUE TO SUDDEN OBSTRUCTION
𝑪𝒄 =
𝑨𝑪
(𝑨−𝒂)
30. S.No. Loss Of Energy Formulae
1 Loss Of Energy Due Sudden
Enlargement 𝒉𝒆 =
𝑽𝟏 − 𝑽𝟐
𝟐
𝟐𝒈
2 Loss Of Energy Due Sudden Contraction
𝐡𝐜 =
𝒌𝑽𝟐
𝟐
𝟐𝒈
Where, 𝒌 =
𝟏
𝑪𝒄
− 𝟏
𝟐
Cc ==
𝑨𝒄
𝑨𝟐
3 Loss Of Energy At Entrance
𝐡𝐢 =
𝟎. 𝟓𝑽𝟏
𝟐
𝟐𝒈
4 Loss Of Energy At Exit
𝐡𝐨 =
𝑽𝟐
𝟐
𝟐𝒈
5 Loss Of Energy Due To Gradual
Contraction And Expansion 𝐡𝐠 =
𝒌 𝑽𝟏 − 𝑽𝟐
𝟐
𝟐𝒈
6 Loss Of Energy Due To Bend In A Pipe
𝐡𝐛 =
𝒌𝑽𝟐
𝟐𝒈
7 Loss Of Energy Due To Various Pipe
Fittings 𝐡𝐯 =
𝒌𝑽𝟐
𝟐𝒈
8 Loss Of Energy Due To Sudden
Obstruction
𝐡𝐨𝐛 =
𝑽𝟐
𝟐𝒈
𝑨
𝑪𝑪(𝑨−𝒂)
− 𝟏 where, 𝑪𝒄 =
𝑨𝑪
(𝑨−𝒂)
31. Water is flowing through a horizontal pipe of diameter 200 mm at a velocity of 3 m/s.
A circular solid plate of diameter 150 mm is placed in the pipe to obstruct the flow.
Find the loss of head due to obstruction in the pipe if Cc = 0.62.
Given:
D = 200 mm = 0.2 m
A =
𝜋
4
D2 =
𝜋
4
0.22 =0.031 m2
V = 3 m/s
d = 150 mm = 0.15 m
a =
𝜋
4
d2 =
𝜋
4
0.152 =0.017 m2
Cc = 0.62
To find:
hob
Solution:
hob =
𝑉2
2𝑔
𝐴
𝐶𝐶(𝐴−𝑎)
− 1
hob =
32
2 ∗9.81
0.031
0.62(0.037−0.017)
− 1
hob = 3.315 m
32. A horizontal pipe line 40 m long is connected to a water tank at one end and discharges freely
into the atmosphere at the other end. For the first 25 m of its length from the tank, the pipe is
150 mm diameter and its diameter is suddenly enlarged to 300 mm. The height of water level in
the tank is 8 m above the center of the pipe. Considering all losses if head which occur,
determine the rate of flow. Take f = 0.01 for both sections of the pipe
Given:
l = 40 m
l1 = 25 m
d1 = 150 mm =0.15 m
l2 = 15 m
d2 = 300 mm = 0.3 m
z = 8 m
f = 0.01
To find:
Q = AV
35. WHEN PIPE ARE CONNECTED SERIES
𝑸 = 𝑸𝟏 = 𝑸𝟐 = 𝑸𝟑
𝑯 = 𝒉𝒇𝟏 + 𝒉𝒇𝟐 + 𝒉𝒇𝟑
Neglecting Minor loss
𝑯 = 𝒉𝒊 + 𝒉𝒇𝟏 + 𝒉𝒄 + 𝒉𝒇𝟐 + 𝒉𝒆 + 𝒉𝒇𝟑 + 𝒉𝒐
Considering Minor loss
36. The difference in water surface levels in two tanks, which are connected by three pipes in series
of lengths 300 m, 170 m and 210 m and of diameters 300 mm, 200 mm and 400 mm respectively
is 12 m. Determine the rate of flow of water if co-efficient of friction are 0.005, 0.0052 and
0.0048 respectively, considering: (i) minor losses also (ii) neglecting minor losses.
Given:
L1 = 300 m; L2 = 170 m; L3 = 210 m
D1 = 300 mm = 0.3m
D2 = 200 mm = 0.2 m
D3 = 400 mm = 0.4 m
H = 12 m
f1 = 0.005
f2 = 0.0052
f3 = 0.0048
To find:
Q
(i) All losses
(ii) Neglect Minor losses
41. Three pipes of lengths 800 m, 500 m and 400 m and of diameters 500 mm, 400 mm and
300 mm respectively are connected in series. These pipes are to be replaced by a single
pipe of length 1700 m. find the diameter of the single pipe.
Given:
L1 = 800 m; L2 = 500 m; L3 = 400 m
L = 1700 m
D1 = 500 mm = 0.5 m; D2 = 400 mm = 0.4 m; D3 = 300 mm = 0.3 m
To find:
D
Solution:
𝐿
𝐷5 =
𝐿1
𝐷1
5 +
𝐿2
𝐷2
5 +
𝐿3
𝐷3
5
1700
𝐷5 =
800
0.52 +
500
0.42 +
400
0.32
D = 0.37 mm
42. WHEN PIPE ARE CONNECTED PARALLEL
𝑸 = 𝑸𝟏 + 𝑸𝟐
𝒉𝒇 = 𝒉𝒇𝟏 = 𝒉𝒇𝟐
43. A pipe of diameter 20 cm and length 2000 m connects two reservoirs, having difference of
water levels as 20 m, Determine the discharge through the pipe. Take f = 0.015 and neglect
minor losses.
Given:
D = 20 cm = 0.2 m
L = 2000 m
H = 20 m
To find:
Q
Solution:
Q = A V
𝑯 =
𝟒×𝒇×𝑳×𝑽𝟐
𝟐×𝒈×𝒅
=> 20 =
𝟒×𝟎.𝟎𝟏𝟓×𝟐𝟎𝟎𝟎×𝑽𝟐
𝟐×𝟗.𝟖𝟏×𝟎.𝟐
=> v = 0.808 m/s
Qold =
𝜋
4
d2 * V => Q = 0.025 m3/s
44. Given:
D1 = 20 cm = 0.2 m
L1 = 800 m
D2 = 20 cm = 0.2 m
L2 = 1200 m
D3 = 20 cm = 0.2 m
L3 = 1200 m
H = 20 m
A1= A2 = A3 =
𝜋
4
d2 =
𝜋
4
0.22 = 0.0314 m2
To find:
Qnew – Qold
If an additional pipe of diameter 20 cm and length 1200 m is attached to the last 1200 m
length of the existing pipe, find the increase in the discharge. Take f = 0.015 and neglect
minor losses.
47. HYDRAULIC ENERGY LINE (OR) HYDRAULIC GRADIENT LINE
❖ It is defined as a line which gives the sum of
pressure head and datum head of flowing fluid in
pipe with respect to some reference line. (H.G.L.)
TOTAL ENERGY LINE (OR) TOTAL GRADIENT LINE
❖ It is defined as a line which gives the sum of
pressure head, datum head and kinetic head of
flowing fluid in pipe with respect to some
reference line. (T.E.L)
48. A horizontal pipe line 40 m long is connected to a water tank at one end and discharges freely
into the atmosphere at the other end. For the first 25 m of its length from the tank, the pipe is
150 mm diameter and its diameter is suddenly enlarged to 300 mm. The height of water level in
the tank is 8 m above the center of the pipe. Considering all losses if head which occur,
determine the rate of flow. Take f = 0.01 for both sections of the pipe. Draw the hydraulic
gradient and total energy line.
Given:
L = 40 m
L1 = 25 m
D1 = 150 mm =0.15 m
L2 = 15 m
D2 = 300 mm = 0.3 m
Z = 8 m
f = 0.01
To find:
Q = AV
𝛾 𝜋 𝜇 𝜌
1
2