CEIC2001 – Fluid Mechanics Notes
Fluid – A substance which is capable of flowing. A fluid is also a substance which has no permanent resistance to change in shape i.e. a solid can resist a shear stress, τ by static deflection; a fluid cannot, any shear stress applied to a fluid will result in the motion of that fluid for as long as the shear stress is applied. τ=FA

Where F = force which is tangent to a surface (shear force), A = area of moving plate in which shear force is applied to. Velocity gradient – is the change of velocity with distance. If applied shear force is changed, the shear stress is also changed, which results in a new velocity gradient being established. dvdy

Boundary conditions of fluids in contact with a wall, the fluid velocity, v = 0. Fluid Continuum – the variation in properties is so smooth that differential calculus can be used to analyse the substance. The physical problem is approached by treating the fluid as a continuous media and using the average effect of many molecules to solve the problems. A fluid may be considered a continuum when there is a large volume of molecules and very little space between them, since fluids take the shape of the volume they are in. Also, the distance between the molecules (mean free path) is very large compared with the molecular diameter. (http://books.google.com.au/books?id=nCnifcUdNp4C&pg=PA295&lpg=PA295&dq=torque%2Bsprinkler%2Bflowing%2Bwater%2Bfluid%2Bmechanics&source=bl&ots=3zBaQQJDqd&sig=eJi8djtyHKmZI8SlDEeevthsMzs&hl=en&ei=1buETfe0IYbRcf7j4ZAD&sa=X&oi=book_result&ct=result&resnum=1&ved=0CBgQ6AEwAA#v=onepage&q&f=false)

...EXAM 1 NOTES
The actual pressure at a given position is called the absolute pressure, and it is measured relative to absolute vacuum (i.e., absolute zero pressure). Most pressure-measuring devices, however, are calibrated to read zero in the atmosphere (Fig. 3–2), and so they indicate the difference between the absolute pressure and the local atmospheric pressure. This difference is called the gage pressure. Pgage = Pabs - Patm
The pressure at a point in afluid has the same magnitude in all directions. (Pressure is a scalar)
Variation of Pressure with Depth
It will come as no surprise to you that pressure in a fluid at rest does not change in the horizontal direction. This can be shown easily by considering a thin horizontal layer of fluid and doing a force balance in any horizontal direction. However, this is not the case in the vertical direction in a gravity field. Pressure in a fluid increases with depth because more fluid rests on deeper layers, and the effect of this “extra weight” on a deeper layer is balanced by an increase in pressure
For a given fluid, the vertical distance \Delta z is sometimes used as a measure of pressure, and it is called the pressure head.
If we take the top of a fluid to be at the free surface of a liquid open to the atmosphere, where the pressure is the atmospheric pressure Patm, then the pressure at a depth h...

...Fluid Report 2
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...

...CHAPTER 1: FLUID PROPERTIES
LEARNING OUTCOMES
At the end of this topic, you should be able to: Define Fluid State differences between solid and fluid Calculate common fluid properties: i. Mass density ii. Specific weight iii. Relative density iv. Dynamic viscosity v. Kinematic viscosity
INTRODUCTION
FluidMechanics
Gas Liquids Statics
i
F 0 F 0
i
Laminar/ Turbulent
Dynamics
, Flows
Compressible/ Incompressible
Air, He, Ar, N2, etc.
Water, Oils, Alcohols, etc.
Stability Pressure Buoyancy
Surface Tension Compressibility Density Viscosity Vapor Pressure
Steady/Unsteady Viscous/Inviscid
Fluid Dynamics: Chapter 1: Chapter 2: Fluid Introduction Statics Rest of Course Fluidmechanics 1. study of forces and motions in fluids 3 2. study of how fluids move and the forces on them
Applications of fluidmechanics
Aerodynamics Bioengineering and biological systems Combustion Energy generation Geology Hydraulics and Hydrology Hydrodynamics Meteorology Ocean and Coastal Engineering Water Resources
History
Archimedes (287-212 B.C.) - calculation of the hydrostatic buoyancy.
Leonardo da Vinci (1500)-calculation of the mass conservation, reduction of flow resistance by form shaping, motion of waves, the...

...16/11/2011
FluidMechanics - 4 Real Fluids
1
Contents
Introduction Objectives Real Fluid Types of Flow Laminar Flow Turbulent Flow
2
1
16/11/2011
Introduction
In the earlier chapter, the basic equations of continuity and energy were introduced and applied to fluid flow cases where the assumption of frictionless flow (or ideal fluid flow) was made. It is now necessary to introduce concepts which enable the extension of the previous work to real fluids in which viscosity is accepted and frictional effects cannot be ignored. The concept of Reynolds number as an indication of flow type will be used extensively.
3
Real Fluid
• In a real fluid viscosity produces resistance to motion by causing shear or friction forces between fluid particles and between these and boundary walls.
• Due to this viscous effects, fluid tends to ‘stick’ to solid surfaces and have stresses within their body. • The inclusion of viscosity allows the existence of two physically distinct flow regimes, known as laminar and turbulent flow.
4
2
16/11/2011
Types of Flow
• Theoretically the physical nature of fluid flow can be categorized into three types, i.e. laminar, transition and turbulent flow. • To predict whether the flow will be laminar, transition or turbulent, it is necessary to...

...Notes For the First Year Lecture Course:
An Introduction to FluidMechanics
School of Civil Engineering, University of Leeds. CIVE1400 FLUIDMECHANICS Dr Andrew Sleigh May 2001 Table of Contents 0.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
CONTENTS OF THE MODULE
Objectives: Consists of: Specific Elements: Books: Other Teaching Resources. Civil Engineering FluidMechanics System of units The SI System of units Example: Units
3
3 3 4 4 5 6 7 7 9
1.
1.1 1.2 1.3 1.4
FLUIDSMECHANICS AND FLUID PROPERTIES
Objectives of this section Fluids Causes of Viscosity in Fluids Properties of Fluids
10
10 10 15 16
2.
2.1 2.2 2.3 2.4
FORCES IN STATIC FLUIDSFluids statics Pressure Pressure Measurement By Manometer Forces on Submerged Surfaces in Static Fluids
19
19 20 28 33
CIVE 1400: FluidMechanics
Contents and Introduction
1
3.
3.1 3.2 3.3 3.4 3.5 3.6 3.7
FLUID DYNAMICS
Uniform Flow, Steady Flow Flow rate. Continuity The Bernoulli Equation - Work and Energy Applications of the Bernoulli Equation The Momentum Equation Application of the Momentum Equation
44
44 47 49 54 64 75 79
4.
4.1 4.2 4.3 4.4
REAL FLUIDS
Laminar and turbulent flow Pressure loss due...

...Continuum Hypothesis in FluidMechanics
The macroscopic behavior of fluids makes them appear to be continuous. However, when viewed at the microscopic scale fluids cannot be viewed as continuous. The fluid under consideration will have molecules bombarding each other. It is not possible to declare the fluid velocity at a point as there is no guarantee that the fluid molecules are present at that point at a particular instant of time. When we calculate the fluid velocity or density at a point it implies that the value is the average fluid velocity or density of the fluid molecules passing through a small volume surrounding that point. The size of the small volume has to be smaller than the physical region under consideration. However, the size of the volume cannot be extremely small. It has to be large enough to make the averaging meaningful.
Fluid can be considered as a continuous medium in situations considering the fluid properties over distances greater than the average spacing between the fluid molecules. In situations where microscopic details of the fluid are important continuum hypothesis does not apply. An example of such a situation can be fluid flowing through a channel whose dimension is equal to the molecule size or mean free paths of the...

...FluidMechanics
Laboratory 2
Report
Robby Joseph
14103508
1.0 Introduction
This experiment was undertaken for the study of flow in pipes and the factors that affect it in both laminar and turbulent regimes. The transitional regime between laminar and turbulent flow will also be studied. The experiment was done using a pipe with a known diameter, and water was pumped in from a tank. Throughout the process, measurements of the quantity of water and time were taken as well as the hydraulic gradient. With these different parameters, the flow rate, Reynolds number and friction factor were able to be calculated for each test for water and mercury. The main purpose of the process was to analyse and identify the regions of laminar flow, and turbulent flow, as well as the transitional region in between. These values enable the calculation of the friction factor of the pipes for specific flow rates.
2.0 Background
The viscosity (µ) in the pipe flow of a fluid produces friction (shear stress) between lumps of fluid as they pass each other. This causes the fluid to cling to the boundary in the flow field.
Reynolds number (Re) is the ratio of fluid momentum to viscous forces.
Re=ρVDμ
This ratio allows the flow of a fluid to be distinguished; this flow can either be laminar, turbulent or transitional.
Laminar flow only occurs when the flow of a fluid is...