Topics:
1. Introduction to Fluid Dynamics
2. Surface and Body Forces
3. Equations of Motion
- Reynold’s Equation
- Navier-Stokes Equation
- Euler’s Equation
- Bernoulli’s Equation
- Bernoulli’s Equation for Real Fluid
4. Applications of Bernoulli’s Equation
5. The Momentum Equation
6. Application of Momentum Equations
- Force exerted by flowing fluid on pipe bend
- Force exerted by the nozzle on the water
7. Measurement of Flow Rate
a). Venturimeter
b). Orifice Meter
c). Pitot Tube
8. Measurement of Flow Rate in Open Channels
a) Notches
b) Weirs
Topics:
1. Introduction to Fluid Dynamics
2. Surface and Body Forces
3. Equations of Motion
- Reynold’s Equation
- Navier-Stokes Equation
- Euler’s Equation
- Bernoulli’s Equation
- Bernoulli’s Equation for Real Fluid
4. Applications of Bernoulli’s Equation
5. The Momentum Equation
6. Application of Momentum Equations
- Force exerted by flowing fluid on pipe bend
- Force exerted by the nozzle on the water
7. Measurement of Flow Rate
a). Venturimeter
b). Orifice Meter
c). Pitot Tube
8. Measurement of Flow Rate in Open Channels
a) Notches
b) Weirs
Reynolds number and geometry concept, Momentum integral equations, Boundary layer equations, Flow over a flat plate, Flow over cylinder, Pipe flow, fully developed laminar pipe flow, turbulent pipe flow, Losses in pipe flow
A fluid is a state of matter in which its molecules move freely and do not bear a constant relationship in space to other molecules.
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.
Fluids are :-
Liquid : blood, i.v. infusions)
Gas : O2 , N2O)
Vapour (transition from liquid to gas) : N2O (under compression in cylinder), volatile inhalational agents (halothane, isoflurane, etc)
Sublimate (transition from solid to gas bypassing liquid state) : Dry ice (solid CO2), iodine
This pdf includes about the submerged bodies and the forces acting on the submerged bodies. Different terminologies are discussed. Definitions of different bodies in the fluid are discussed as well.
It is small pdf with great knowledge, hope it will be helpful to the students.
Fluid mechanics is a science in study the fluid of liquids and gases in the cases of silence and movement and the forces acting on them can be divided materials found in nature into two branches.
B.TECH. DEGREE COURSE
SCHEME AND SYLLABUS
(2002-03 admission onwards)
MAHATMA GANDHI UNIVERSITY,mg university, KTU
KOTTAYAM
KERALA
Module 1
Introduction - Proprties of fluids - pressure, force, density, specific weight, compressibility, capillarity, surface tension, dynamic and kinematic viscosity-Pascal’s law-Newtonian and non-Newtonian fluids-fluid statics-measurement of pressure-variation of pressure-manometry-hydrostatic pressure on plane and curved surfaces-centre of pressure-buoyancy-floation-stability of submerged and floating bodies-metacentric height-period of oscillation.
Module 2
Kinematics of fluid motion-Eulerian and Lagrangian approach-classification and representation of fluid flow- path line, stream line and streak line. Basic hydrodynamics-equation for acceleration-continuity equation-rotational and irrotational flow-velocity potential and stream function-circulation and vorticity-vortex flow-energy variation across stream lines-basic field flow such as uniform flow, spiral flow, source, sink, doublet, vortex pair, flow past a cylinder with a circulation, Magnus effect-Joukowski theorem-coefficient of lift.
Module 3
Euler’s momentum equation-Bernoulli’s equation and its limitations-momentum and energy correction factors-pressure variation across uniform conduit and uniform bend-pressure distribution in irrotational flow and in curved boundaries-flow through orifices and mouthpieces, notches and weirs-time of emptying a tank-application of Bernoulli’s theorem-orifice meter, ventury meter, pitot tube, rotameter.
Module 4
Navier-Stoke’s equation-body force-Hagen-Poiseullie equation-boundary layer flow theory-velocity variation- methods of controlling-applications-diffuser-boundary layer separation –wakes, drag force, coefficient of drag, skin friction, pressure, profile and total drag-stream lined body, bluff body-drag force on a rectangular plate-drag coefficient for flow around a cylinder-lift and drag force on an aerofoil-applications of aerofoil- characteristics-work done-aerofoil flow recorder-polar diagram-simple problems.
Module 5
Flow of a real fluid-effect of viscosity on fluid flow-laminar and turbulent flow-boundary layer thickness-displacement, momentum and energy thickness-flow through pipes-laminar and turbulent flow in pipes-critical Reynolds number-Darcy-Weisback equation-hydraulic radius-Moody;s chart-pipes in series and parallel-siphon losses in pipes-power transmission through pipes-water hammer-equivalent pipe-open channel flow-Chezy’s equation-most economical cross section-hydraulic jump.
Hydraulic consists of the application of fluid mechanics to water flowing in an isolated environment (pipe, pump) or in an open channel (river, lake, ocean). Civil engineers are primarily concerned with open channel flow, which is governed by the interdependent interaction between the water and the channel. Applications include the design of hydraulic structures, such as sewage conduits, dams and breakwaters, the management of waterways, such as erosion protection and flood protection, and environmental management, such as prediction of the mixing and transport of pollutants in surface water.
Reynolds number and geometry concept, Momentum integral equations, Boundary layer equations, Flow over a flat plate, Flow over cylinder, Pipe flow, fully developed laminar pipe flow, turbulent pipe flow, Losses in pipe flow
A fluid is a state of matter in which its molecules move freely and do not bear a constant relationship in space to other molecules.
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.
Fluids are :-
Liquid : blood, i.v. infusions)
Gas : O2 , N2O)
Vapour (transition from liquid to gas) : N2O (under compression in cylinder), volatile inhalational agents (halothane, isoflurane, etc)
Sublimate (transition from solid to gas bypassing liquid state) : Dry ice (solid CO2), iodine
This pdf includes about the submerged bodies and the forces acting on the submerged bodies. Different terminologies are discussed. Definitions of different bodies in the fluid are discussed as well.
It is small pdf with great knowledge, hope it will be helpful to the students.
Fluid mechanics is a science in study the fluid of liquids and gases in the cases of silence and movement and the forces acting on them can be divided materials found in nature into two branches.
B.TECH. DEGREE COURSE
SCHEME AND SYLLABUS
(2002-03 admission onwards)
MAHATMA GANDHI UNIVERSITY,mg university, KTU
KOTTAYAM
KERALA
Module 1
Introduction - Proprties of fluids - pressure, force, density, specific weight, compressibility, capillarity, surface tension, dynamic and kinematic viscosity-Pascal’s law-Newtonian and non-Newtonian fluids-fluid statics-measurement of pressure-variation of pressure-manometry-hydrostatic pressure on plane and curved surfaces-centre of pressure-buoyancy-floation-stability of submerged and floating bodies-metacentric height-period of oscillation.
Module 2
Kinematics of fluid motion-Eulerian and Lagrangian approach-classification and representation of fluid flow- path line, stream line and streak line. Basic hydrodynamics-equation for acceleration-continuity equation-rotational and irrotational flow-velocity potential and stream function-circulation and vorticity-vortex flow-energy variation across stream lines-basic field flow such as uniform flow, spiral flow, source, sink, doublet, vortex pair, flow past a cylinder with a circulation, Magnus effect-Joukowski theorem-coefficient of lift.
Module 3
Euler’s momentum equation-Bernoulli’s equation and its limitations-momentum and energy correction factors-pressure variation across uniform conduit and uniform bend-pressure distribution in irrotational flow and in curved boundaries-flow through orifices and mouthpieces, notches and weirs-time of emptying a tank-application of Bernoulli’s theorem-orifice meter, ventury meter, pitot tube, rotameter.
Module 4
Navier-Stoke’s equation-body force-Hagen-Poiseullie equation-boundary layer flow theory-velocity variation- methods of controlling-applications-diffuser-boundary layer separation –wakes, drag force, coefficient of drag, skin friction, pressure, profile and total drag-stream lined body, bluff body-drag force on a rectangular plate-drag coefficient for flow around a cylinder-lift and drag force on an aerofoil-applications of aerofoil- characteristics-work done-aerofoil flow recorder-polar diagram-simple problems.
Module 5
Flow of a real fluid-effect of viscosity on fluid flow-laminar and turbulent flow-boundary layer thickness-displacement, momentum and energy thickness-flow through pipes-laminar and turbulent flow in pipes-critical Reynolds number-Darcy-Weisback equation-hydraulic radius-Moody;s chart-pipes in series and parallel-siphon losses in pipes-power transmission through pipes-water hammer-equivalent pipe-open channel flow-Chezy’s equation-most economical cross section-hydraulic jump.
Hydraulic consists of the application of fluid mechanics to water flowing in an isolated environment (pipe, pump) or in an open channel (river, lake, ocean). Civil engineers are primarily concerned with open channel flow, which is governed by the interdependent interaction between the water and the channel. Applications include the design of hydraulic structures, such as sewage conduits, dams and breakwaters, the management of waterways, such as erosion protection and flood protection, and environmental management, such as prediction of the mixing and transport of pollutants in surface water.
FMM- UNIT I FLUID PROPERTIES AND FLOW CHARACTERISTICSKarthik R
Units and dimensions- Properties of fluids- mass density, specific weight, specific volume,
specific gravity, viscosity, compressibility, vapor pressure, surface tension and capillarity. Flow
characteristics – concept of control volume - application of continuity equation, energy
equation and momentum equation.
Ideal fluid:
a fluid with no friction
Also referred to as an inviscid (zero viscosity) fluid
Internal forces at any section within are normal (pressure forces)
Practical applications: many flows approximate frictionless flow away from solid boundaries.
Real Fluids
Tangential or shearing forces always develop where there is motion relative to solid body
Thus, fluid friction is created
Shear forces oppose motion of one particle past another
Friction forces gives rise to a fluid property called viscosity
Unit 3 introduction to fluid mechanics as per AKTU KME101TVivek Singh Chauhan
strictly following syllabus of KME 101T of AKTU for first yr 2021
fluid properties, bernoulli's equation with proof and numericals , pumps, turbine , hydraulic lift, continuity equation
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
COLLEGE BUS MANAGEMENT SYSTEM PROJECT REPORT.pdfKamal Acharya
The College Bus Management system is completely developed by Visual Basic .NET Version. The application is connect with most secured database language MS SQL Server. The application is develop by using best combination of front-end and back-end languages. The application is totally design like flat user interface. This flat user interface is more attractive user interface in 2017. The application is gives more important to the system functionality. The application is to manage the student’s details, driver’s details, bus details, bus route details, bus fees details and more. The application has only one unit for admin. The admin can manage the entire application. The admin can login into the application by using username and password of the admin. The application is develop for big and small colleges. It is more user friendly for non-computer person. Even they can easily learn how to manage the application within hours. The application is more secure by the admin. The system will give an effective output for the VB.Net and SQL Server given as input to the system. The compiled java program given as input to the system, after scanning the program will generate different reports. The application generates the report for users. The admin can view and download the report of the data. The application deliver the excel format reports. Because, excel formatted reports is very easy to understand the income and expense of the college bus. This application is mainly develop for windows operating system users. In 2017, 73% of people enterprises are using windows operating system. So the application will easily install for all the windows operating system users. The application-developed size is very low. The application consumes very low space in disk. Therefore, the user can allocate very minimum local disk space for this application.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
4. What is Fluid Mechanics?
It is the science that deals with the behavior of fluids
at rest or in motion, and the interaction of fluids with
solids or other fluids at the boundaries.
5. Focus on rate of flow and the various
pressures that inhibit them
6. What is a Fluid?
A fluid is a substance that deforms when subjected to
force.
Liquids occupy definite volumes; gases expand to occupy
any containing vessel
7. The Concept of a Fluid
A solid can resist a shear stress by a static deformation; a fluid
cannot.
The fluid moves and deforms continuously as long as the shear
stress is applied.
11. Dimensions and Units
A dimension is the measure by which a physical variable is
expressed quantitatively.
A unit is a particular way of attaching a number to the
quantitative dimension.
12. Primary Dimensions
In fluid mechanics there are only four primary dimensions from
which all other dimensions can be derived: mass, length, time, and
temperature.
17. FLUID PROPERTIES
The Velocity Field
Foremost among the properties of a flow is the velocity field
V(x, y, z, t).
In fact, determining the velocity is often tantamount to solving a
flow problem, since other properties follow directly from the velocity
field.
20. FLUID PROPERTIES
Unit weight / Specific Weight
◦ Weight per unit volume of a fluid
γ =
𝒘
𝑽
Where:
γ = unit wt. (N/m3, lbf/ft3)
w = weight of fluid (N, lbf)
V = volume (m3, ft3)
21. FLUID PROPERTIES
Mass Density
◦ Mass per unit volume of a fluid
ρ =
𝒎
𝑽
; ρair = 1.205 kg/m3; ρwater = 1000 kg/m3
Where:
ρ = density (kg/m3, lb/ft3)
m = mass of fluid (kg, lb)
V = volume (m3, ft3)
22. FLUID PROPERTIES
Density of Gases
ρ =
𝒑
𝑹𝑻
Where:
ρ = density (kg/m3)
p = absolute pressure of gas (kPa)
R = gas constant (J/kg-K)
T = absolute temperature (K)
23. FLUID PROPERTIES
Specific Gravity
◦ Unit wt. of fluid divided by the unit wt. of water
s =
𝜸(𝒇)
𝜸(𝒘)
Where:
s = specific gravity (dmls)
𝜸(𝒇) = unit wt. of fluid (N/m3)
𝜸(𝒘) = unit wt. of water (N/m3)
24. FLUID PROPERTIES
Viscosity – resistance to deformation which causes flow
◦ Kinematic Viscosity
ν =
𝝁
𝝆
Where:
ν = (nu) k. viscosity (m2/s or stoke)
𝝁 = dynamic/absolute viscosity (Pa*s)
𝝆 = density (kg/m3) 1 stoke = 1 cm2/s
27. FLUID PROPERTIES
Viscosity is a proportionality
constant suggesting a linear
relationship between shear
stress and velocity gradient.
28. FLUID PROPERTIES
Surface Tension
◦ The surface tension of a fluid is the work that must be done to
bring enough molecules from inside the liquid to the surface to
form a new unit area of that surface in ft-lb/ft2 or N-m/m2.
29. FLUID PROPERTIES
Capillarity
◦ Rise or fall of fluid in for example a tube which is caused by
surface tension and depends on the relative magnitudes of the
cohesion of the fluid and its adhesion to the walls.
Rise – cohesion < adhesion
Fall – cohesion > adhesion
35. Ideal Fluids
Assumed to have no viscosity (no resistance to shear)
Incompressible
Have no uniform velocity when flowing
No friction b/w moving layers of fluid
No eddy currents or turbulence
36. Real Fluids
Exhibit infinite viscosities
Non-uniform velocity distribution when flowing
Compressible
Experience friction and turbulence in flow
37. Newtonian Fluids
◦Newtonian fluids show linear relationship
between shear stress (τ) and velocity gradient
(du/dy) – that is the viscosity remains constant
irrespective of changes to shear stress and
velocity gradient
38. Non-Newtonian Fluids
◦The ratio between shear stress (τ) and velocity
gradient (du/dy) or shear rate is not constant but
depends on the shear force exerted on the fluid.
◦Non-Newtonian fluids doesn’t show linearity
between shear stress and shearing rate (velocity
gradient).
39. Non-Newtonian Fluids
Bingham Fluids - has true shear rate (damp clay, concentrated slurries,
cheese)
Pseudoplastics – viscosity decreases as shear rate increases (paint,
mayonnaise, blood, heavy slurries)
Dilatent fluids – viscosity increases as shear rate increases (most honeys,
sand)
Thixiotropic – become more fluid (viscosity decreases) when being more
stirred with time
Rheopetic – become less fluid with time, opposite of thixiotropic
40. Most fluid problems assume real fluids with Newtonian
characteristics for convenience. This assumption is appropriate
for:
water
air
gases
steam
simple fluids: alcohol, gasoline, acid solutions
42. Unit Pressure or Pressure (p)
Pressure - is the force per unit area exerted by a liquid or
gad on a body or surface, with the force acting at right
angles to the surface uniformly in all directions.
Where:
p = pressure, N/m2 or Pa (psf, psi)
F = force, N or lbf
A = area, m2 or ft2 or in2
𝑝 =
𝐹
𝐴
43. Pascal’s Law
States that the pressure entity at a point in a fluid at rest is
the same in all directions
P1 = P2 =P3
46. Hydrostatic Pressure Distribution
Pressure in a continuously distributed uniform
static fluid varies only with vertical distance and
is independent of the shape of the container.
The pressure is the same at all points on a
given horizontal plane in the fluid. The pressure
increases with depth in the fluid
47.
48. Absolute and Gage Pressures
Absolute pressure is the pressure above absolute zero (vacuum - no
air). It is the lowest possible pressure attainable. It can never be
negative value.
Gage pressure is pressure above or below the atmosphere and can
be measured by pressure gauges or manometers. The smallest gage
pressure is equal to the negative of ambient atmospheric pressure.
Atmospheric pressure is the pressure at any one point on the earth’s
surface from the weight of the air above it.
63. Steps in Solving Manometer Problems
1. Decide on the fluid in feet or meter, of which the heads are to be
expressed.
2. Starting from an end point, number in order, the interface of
different fluids.
3. Identify points of equal pressure. Label these points with the same
number.
4. Proceed from level to level, adding (if going down) or subtracting
(if going up) pressure heads as the elevation decreases or increases,
respectively with due regard for the specific gravity of the fluids.
76. Hydrostatic Forces on Surfaces
1. Hydrostatic forces on plane surfaces
2. Hydrostatic forces on curved surfaces
3. Hydrostatic forces in layered surfaces
77. Hydrostatic Forces on Plane Surfaces
If the pressure over a plane area is uniform, as in
the case of a horizontal surface submerged in a
liquid, the total hydrostatic force/pressure is given by:
F= 𝑝𝐴
78. Hydrostatic Forces on Plane Surfaces
For an inclined or vertical plane submerged in a
liquid, the total pressure is given by:
Lifted from Fluid Mech. &
Hydraulics 4th Ed. By Gillesania
80. Hydrostatic Forces on Plane Surfaces
The hydrostatic problem is reduced to simple formulas
involving centroid and moments of inertia of the plate cross-
sectional area.
Lifted from Fluid Mechanics 3rd Ed. by
White
89. Hydrostatic Forces on Curved Surfaces
The resultant force on a curved surface is most easily computed
by separating it into horizontal and vertical components.
Lifted from Fluid Mechanics 3rd
Ed. by White
90. Hydrostatic Forces on Curved Surfaces
The horizontal component of force on a curved surface equals the
force on the plane area formed by the projection of the curved surface
onto a vertical plane normal to the component.
The vertical component of pressure force on a curved surface equals
in magnitude and direction the weight of the entire column of fluid,
both liquid and atmosphere, above the curved surface.
98. Hydrostatic Forces on Layered Surfaces
If the fluid is layered with different
densities, a single formula cannot solve
the problem because the slope of the
linear pressure distribution changes
between layers.
However, the formulas apply separately
to each layer, and thus the appropriate
remedy is to compute and sum the
separate layer forces and moments.
Lifted from Fluid Mechanics 3rd
Ed. by White
113. Open Channel Flow
The flow of liquids in a pipe is partially filled
with the liquid and there is a free surface
114. PRISMATIC VS. NON-PRISMATIC
A prismatic channel is a channel built with
constant cross-section and constant bottom
slope
Otherwise, it is a non-prismatic channel,
characterized by non-uniform cross section and
slope.
115. Artificial channels such as rectangular, trapezoid,
parabola and circle are the most commonly used
prismatic channels.
Natural channels are usually non-prismatic.
116. FLOW CLASSIFICATION
1. TIME AS THE CRITERION
2. SPACE AS THE CRITERION
3. BASED ON FLOW REGIMES
STEADY FLOW/UNSTEADY FLOW
UNIFORM FLOW/NON-UNIFORM FLOW
INERTIAL FORCES
VISCOUS FORCES
GRAVITATIONAL FORCES
117.
118. Incompressible vs. Compressible
•Incompressible fluids maintain a nearly constant
density at given temperatures and pressures. Density
changes should be under 5%.
•Compressible fluids have significantly varying
densities during the flow
119. While all flows are compressible, flows are usually
treated as being incompressible when the Mach
number (the ratio of the speed of the flow to the speed
of sound) is less than 0.3 (30%)
Compressibility is NOT a fluid property but a flow
property.
120. Viscous vs. Inviscid Flow
Flows in which the effects of viscosity are significant
are called viscous flows.
Idealized flows of zero-viscosity fluids are called
frictionless or inviscid flows. The effects of viscosity is
very small.
121. Laminar vs. Turbulent Flow
The highly ordered fluid motion characterized by
smooth streamlines is called laminar.
The highly disordered fluid motion that typically
occurs at high velocities characterized by velocity
fluctuations is called turbulent.
122. Laminar vs. Turbulent Flow
Laminar: high-viscosity fluid such as oil at low velocity
Turbulent: low viscosity fluid such as air at high
velocity
125. Internal vs. External Flow
◦A fluid flow is classified as being internal and external,
depending on whether the fluid is forced to flow in a
confined channel or over a surface.
126. Internal Flow
The flow in a pipe or duct in which the fluid is
completely bounded by solid surfaces.
129. External Flow – The Boundary Layer
is the flow of an unbounded fluid
over a surface
130. Velocity Boundary Layer
The x-coordinate is measured along the plate surface from the leading
edge of the plate in the direction of the flow, and y is measured from
the surface in the normal direction.
The velocity of the particles in the first fluid layer adjacent to the plate
becomes zero because of the no-slip condition.
Thus, the presence of the plate is felt up to some normal distance from
the plate beyond which the free-stream velocity u remains essentially
unchanged.
131. Natural vs. Forced Flow
A fluid flow is said to be natural or forced, depending on how the fluid motion
is initiated.
In forced flow, a fluid is forced to flow over a surface or in a pipe by external
means such as a pump or a fan.
In natural flows, any fluid motion is due to a natural means such as the
buoyancy effect, which manifests itself as the rise of the warmer (and thus
lighter) fluid and the fall of cooler (and thus denser) fluid.
132. Steady vs. Unsteady (Transient) Flow
The term steady implies no change with time. The opposite
of steady is unsteady, or transient.
Many devices such as turbines, compressors, boilers,
condensers, and heat exchangers operate for long periods of
time under the same conditions, and they are classified as
steady-flow devices.
134. Reynold’s Number
The transition from laminar to turbulent flow depends on
the surface geometry, surface roughness, free-stream
velocity, surface temperature, and type of fluid, among
other things.
After exhaustive experiments in the 1880s, Osborn Reynolds
discovered that the flow regime depends mainly on the
ratio of the inertia forces to viscous forces in the fluid.
135. REYNOLDS NO.
LAMINAR FLOW
◦Re < 500
TURBULENT FLOW
◦Re > 1,000
TRANSITION FLOW
◦500 < Re < 1,000
VL
Re
English Units
136. LAMINAR FLOW
Re < 2130
TURBULENT FLOW
Re > 4000
TRANSITION FLOW
2130 < Re < 4000
S.I. Units
137. Reynold’s Number
At large Reynolds numbers, the inertia forces, which are
proportional to the density and the velocity of the fluid, are large
relative to the viscous forces, and thus the viscous forces cannot
prevent the random and rapid fluctuations of the fluid.
At small Reynolds numbers, however, the viscous forces are large
enough to overcome the inertia forces and to keep the fluid “in line.”
The Reynolds number at which the flow becomes turbulent is called
the critical Reynolds number.
138. Reynold’s Number
For flow over flat plate:
where xcr is the distance from the leading edge of the
plate at which transition from laminar to turbulent flow
occurs
139.
140. Streamlined vs. Turbulent Flow
Streamlined flow is when fluid moves in parallel elements,
depicted by streamlines. The velocity of any element is
constant but not necessarily the same as that of an adjacent
element.
Turbulent flow is when the fluid moves in elemental swirls or
eddies. Both velocity and direction of each element change
over time, thus a violent mixing results.
143. Darcy-Weisbach Equation
relates the head loss, or pressure loss, due to friction along a given
length of pipe to the average velocity of the fluid flow for an
incompressible fluid
hf =
𝟒𝒇𝑳
𝑫
𝒙 (𝑽𝟐)
𝟐𝒈
146. Cavitation
the vaporization that may occur at locations
where the pressure drops below the vapor
pressure
Cavities are known as “bubbles” or “voids”