In the derivation of Bernoulli’s equation, the assumption of the inviscid and incompressible flow is used. However in the real case, the viscosity cannot be neglect and the density of the flow is not always constant. Thus Bernoulli’s equation is not always correct. For the lab, it is reasonable to assume the flow is inviscid and incompressible. Firstly, the pitot was placed at the center of the flow. The skin friction (effect of viscosity) is inversely proportional to distance. Therefore the effect of viscosity can be neglected in the pitot. Secondly, the speed of the flow is much lower than the speed of sound under the sonic condition. Therefore, the Mach number is low enough to neglect the change of density of the controlled volume and the controlled volume is almost incompressible. That is why we can estimate the velocity of the flow by Bernoulli’s equation and continuity equation.
As a result of the viscosity, the internal flow is constrained by the bounding walls and the effect grows during the entire flow. At the inflow region, the flow is nearly inviscid. After that, the boundary layers are growing along the duct which is called developing profile region. This is because the effect of viscosity is growing. At the centre of the duct, there is an inviscid core flow. When the boundary layers are merged, the flow is fully developed and the velocity is not affected by viscosity anymore. Meanwhile the static pressure decreases due to the effect of viscosity (friction). The expanding area of diffuser produces low velocity, which increases the pressure and adverse gradient. The fluid is viscid and the boundary layer is separated as a result of the back flow and poor pressure recovery, if the angle is large. The separation will increase the flow losses. Besides, the larger angle leads to the earlier separation and heavier flow losses. If there is an abrupt enlargement, because of viscosity, large vortex flow causes the flow losses and...
...Experiment 3: Fluid Flow Friction and Fitting Loss
Objective
To determine the pressure or head loss in different diameters pipes, joints and valves
Theory
Pipe flows belong to a broader class of flows, called internal flows, where the fluid is completely bounded by solid surfaces. In contrast, in external flows, such as flow over a flat plate or an airplane wing, only part of the flow is bounded by a solid surface. The term pipe flow is generally used to describe flow through round pipes, ducts, nozzles, sudden expansions and contractions, valves and other fittings. When a gas or a liquid flows through a pipe, there is a loss of pressure in the fluid, because energy is required to overcome the viscous or frictional forces exerted by the walls of the pipe on the moving fluid. In addition to the energy lost due to frictional forces, the flow also loses energy (or pressure) as it goes through fittings, such as valves, elbows, contractions and expansions. This loss in pressure is mainly due to the fact that flow separates locally as it moves through such fittings. The pressure loss in pipe flows is commonly referred to as head loss. When a fluid flows through pipes, energy is lost inevitably due to frictions which occur as a result of viscous drag. Fluid friction produces eddies and turbulence, and these form of kinetic energy are eventually converted into thermal energy. Losses in...
...Egon Krause Fluid Mechanics
Egon Krause
Fluid Mechanics
With Problems and Solutions, and an Aerodynamic Laboratory
With 607 Figures
Prof. Dr. Egon Krause RWTH Aachen Aerodynamisches Institut W¨ llnerstr.57 u 52062 Aachen Germany
ISBN 3540229817 Springer Berlin Heidelberg New York
Library of Congress Control Number: 2004117071 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, speciﬁcally the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microﬁlm or in other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from SpringerVerlag. Violations are liable to prosecution under German Copyright Law. Springer is a part of Springer Science+Business Media springeronline.com
c SpringerVerlag Berlin Heidelberg 2005 Printed in Germany
The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a speciﬁc statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Data conversion by the authors. Final processing by PTPBerlin ProtagoTEXProduction GmbH, Germany CoverDesign:...
...f NHYDRAULICS 1 (HYDRODYNAMICS)
SPRING 2005
Part 1. FluidFlow Principles
1. Introduction
1.1 Definitions
1.2 Notation and fluid properties
1.3 Hydrostatics
1.4 Fluid dynamics
1.5 Control volumes
1.6 Visualising fluid flow
1.7 Real and ideal fluids
1.8 Laminar and turbulent flow
2. Continuity (mass conservation)
2.1 Flow rate
2.2 The steady continuity equation
2.3 Unsteady continuity equation
3. The Equation of Motion
3.1 Forms of the equation of motion
3.2 Fluid acceleration
3.3 Bernoulli’s equation
3.4 Application to flow measurement
3.5 Other applications (flow through an orifice; tankemptying)
4. The Momentum Principle
4.1 Steadyflow momentum principle
4.2 Applications (pipe contractions; pipe bends; jets)
5. Energy
5.1 Derivation of Bernoulli’s equation from an energy principle
5.2 Fluid head
5.3 Departures from ideal flow (discharge coefficients; loss coefficients; momentum & energy coefficients)
Part 2. Applications (Separate Notes)
1. Hydraulic Jump
2. Pipe Flow (Dr LaneSerff)
Recommended Reading
Hamill, 2001, Understanding Hydraulics, 2nd Edition, Palgrave, ISBN 0333779061
Chadwick, Morfett and Borthwick, 2004, Hydraulics in Civil and Environmental
Engineering, 4th Edition, Spon Press, ISBN 0415306094
Massey, 1998, Mechanics of Fluids, 7th Edition, (Revised by WardSmith, J.), Stanley
Thornes,...
...Experiment 1
Fluid Flow In A Smooth Pipe
Abstract
In this experiment, three variable flow meters are used to alter the flowrate. Changes in pressure drop due to the change in flowrate are then observed from the three pressure gauges that can measure pressure at different range and recorded. The shift from laminar flow to turbulent flow is seen from the results recorded, but it is observed more clearly from the watersoluble dye experiment that was carried out by the demonstrator. Laminar flow turns to be turbulent when the Reynolds Number goes above a certain value, around 2000.
Aims
To look at how the pressure drop changes when the average velocity is altered in a circular pipe and to plot a graph of Friction Factor versus Reynolds Number. Another aim is to examine the shift from laminar flow to turbulent flow.
Schematic Diagram
Water Out
Inverted Waterair Manometer
Wetwet Digital Differential Pressure (0100kPa)
Capsuhelic Differential Pressure (0250kPa)
1600 L/hr
250 L/hr
70 L/hr
1.5m
Water In
watersoluble dye
P
P
P
Figure 1: Schematic Diagram of Apparatus Used and Direction of Flow in a Smooth Pipe
Results
A graph of log  log plot of f versus Re is plotted, and a straight line of best fit through the data points for laminar flow is drawn:
Figure 2: Graph of log  log plot of f versus Re
Discussions
To calculate the slope of the best fit line from Figure 2, two points are selected: (600, 0.02) and (200, 0.07)...
...WHAT IS FLUID MECHANICS ?
FLUIED:
Any thing whose particles can move easily from one place to another that means shape can be easily changed upon the application of negligible force.
MECHANICS:
Study of response of bodies upon the application of force.
FLUID MECHANICS :
Fluid mechanics may be defined as the branch of engineering science which deal with behavior of fluids under the condition of rest and motion.
FLUID MECHANICS DIVIDED IN 3 PARTS
1 STATICS
2 KINAMETICS
3 DYNAMICS
STATICS:
Study of incompressible fluids under static conditions is called hydrostatic and that branch dealing compressible static gasses is termed as aerostatics.
KINAMETICS:
It deal with velocities acceleration and the pattern of flow only forces or energy, velocity and acceleration .
DYNAMICS:
It deals with the relation b/w velocities acceleration of fluid with the force or energy causing them.
WRITE DOWN THE PROPERTIES OF FLUIED?
The matter can be classified on the basis of spacing b/w the molecules of matter as
1 SOLID STATE:
2 FLUIED STATE.
I LIQUID STATE
ii GASES STATE
In...
...objective of this lab was to find and examine the viscosities of ideal and nonideal solutions. The ideal being the toluene/pxylene and the nonideal being the methanol/water. The second objective of this lab was to investigate the temperature dependence of viscosity (Halpern, 171).
Introduction:
Viscosity is the resistance to flow of a certain fluid. In this experiment two solutions are used. According to the definition of viscosity mobile liquids have a relatively low viscosity. Fluidity is the reciprocal of viscosity, given as equation 1: F=1/ η. Fluidity is advantageous because solutions of mixed solutions of nonassociating liquids are roughly additive. In this experiment binary solutions are used, so if each pure liquid has fluidities Fa and Fb, the fluidity of a mixture is given by: Equation1 (Halpern, 173).
F=xAFA•+xBFB• where Xa and Xb are the mole fractions.
The viscosity of the mixture is given as:
ln η = XA ln η •A + XB ln η •B Equation 2 (Halpern, 173)
The second part of this lab is to measure the temperature dependence of viscosity. It is known that the viscosity of a pure liquid will increase exponentially. If the flow time of a liquid is measures and the density is known the...
...plane model. Testing of models is imperative in the design
of complex, expensive fluidsengineering devices. Such tests use the principles of dimensional
analysis and modeling from this chapter. (Courtesy of Mark E. Gibson/Visuals Unlimited)

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Textbook Table of Contents

Study Guide
Chapter 5
Dimensional Analysis
and Similarity
Motivation. In this chapter we discuss the planning, presentation, and interpretation
of experimental data. We shall try to convince you that such data are best presented in
dimensionless form. Experiments which might result in tables of output, or even multiple volumes of tables, might be reduced to a single set of curves—or even a single
curve—when suitably nondimensionalized. The technique for doing this is dimensional
analysis.
Chapter 3 presented gross controlvolume balances of mass, momentum, and energy which led to estimates of global parameters: mass flow, force, torque, total heat
transfer. Chapter 4 presented infinitesimal balances which led to the basic partial differential equations of fluid flow and some particular solutions. These two chapters covered analytical techniques, which are limited to fairly simple geometries and welldefined boundary conditions. Probably onethird of fluidflow problems can be attacked
in this analytical or theoretical manner.
The other twothirds of all fluid problems are too...
...PLANNING INTERVENTION RATIONALE EVALUATION 
      
SUBJECTIVE: Fluid volume deficit related to SHORT TERM GOAL: >Establish rapport. >To gain the pt’s trust SHORT TERM GOAL: 
“Sumusuka siya ng 3 beses at excessive vomiting and loose After the shift, the patient   After 30 minutes of rendered 
dumudumi ng madami,” as watery stool will be able to restore its   care, the patient had restored 
verbalized by patient’s mother.  normal circulating body fluids >Monitor vital signs. >To obtain baseline data his body’s circulating fluids. 
      
OBJECTIVE:  LONG TERM GOAL: ...