Table of Contents
INTRODUCTION3
Method:3
Part 23
Part 33
Part 44
Part 54
RESULTS4
Part 14
Part 26
Part 36
Part 46
Part 5:6
DISCUSSION7
CONCLUSION7
REFERENCES7

INTRODUCTION
The main objective of this assignment is to simulate a 3-D air flow in a pipe using Ansys CFX. The pipe was simulated under specific conditions. These conditions are air temperature to be 25⁰C (degrees Celsius), one atmospheric reference pressure, no heat transfer and laminar flow. The results from the simulation of laminar flow in the pipe were compared with the theoretical ones. Also the mesh was refined in the simulation to see if it is possible to get more accurate results using grid convergence analysis. Method:

The pipe used in the simulation has dimensions of a 0.5m axial length and a radial diameter of 12mm. The air entering the pipe, inlet velocity, is set to 0.4 m/s at a temperature of 25⁰C and one atmospheric pressure. No slip condition was set on the pipe walls. The outlet of pipe was set to zero gauge average static pressure. In CFX a mesh was formed on the pipe with a default mesh spacing (element size) of 2mm. Figure (1) and (2) shows the setup of the model before simulation was preformed Figure 1: Mesh without Inflation

Figure 1: Mesh without Inflation

Figure 2: Mesh with Inflation

Part 2
Calculating the pressure drop Δp=fLDρ Ub22Equation (1) Calculating Reynolds number Re=UbD/μ Equation (2) Friction Factorf=64/ReEquation (3)

The results were calculated using excel, and plotted in Figure (3). Part 3
Estimating the entrance pipe length Le: Le/D=0.06ReEquation (4) Having Re=UbD/μEquation (3)
The simulated results of velocity vs. axial length were plotted in Figure (5). From the graph the Le (entrance pipe length) was determined by estimating the point in the x-axis where the curve is straight horizontal line. Part 4

...compared to exact solution. In the next steps, the validation, stability and
effects of changing boundary condition on our solution will be investigated. Finally, the results
will be presented and completely discussed.
Programming Assignment 2-Wave Equation
1. Introduction
The wave equation is an important second-order linear partial differential equation for the
description of waves – as they occur in physics – such as sound waves, light waves and
water waves. It arises in fields like acoustics, electromagnetic, and fluiddynamics. Historically,
the problem of a vibrating string such as that of a musical instrument was studied by Jean le
Rond d'Alembert, Leonhard Euler, Daniel Bernoulli, and Joseph-Louis Lagrange.
Figure 1-Wave Diffusion
Wave equation has many applications. The ideal-string wave equation applies to any perfectly
elastic medium which is displaced along one dimension. For example, the air column of a
clarinet or organ pipe can be modeled using the one-dimensional wave by substituting airpressure deviation for string displacement, and longitudinal volume velocity for transverse
string velocity.
Wave equations are examples of hyperbolic partial differential equations, but there are many
variations. In its simplest form, the wave equation concerns a time variable, one or more spatial
variables, and a scalar function, whose values could model the displacement of a wave.
As mentioned in...

...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 water-soluble 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 Water-air Manometer
Wet-wet Digital Differential Pressure (0-100kPa)
Capsuhelic Differential Pressure (0-250kPa)
1600 L/hr
250 L/hr
70 L/hr
1.5m
Water In
water-soluble 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,...

...FluidDynamics
– Viscosity
Dave Foster
Department of Chemical Engineering
University of Rochester
Email: dafoster@che.rochester.edu
1
Chemical Engineering
What do Chemical Engineers Do?
Manufacturing
Research
Biotech
Chemical
Pharmaceutical
Medical
2
OK, first a little background
Fluid Mechanics is the study of fluids either in
motion (FluidDynamics) or at rest (Fluid Statics)
Fluids are either gas or liquid
Solids are NOT fluids
Properties of the fluid are things like density,
pressure, temperature, and VISCOSITY!
3
Fluid – a definition
A substance that deforms continuously under
the action of shear stress
Gas or Liquid
Solids can resist a shear stress, a fluid can’t
4
Applications of Fluid Mechanics
Explains blood flow in capillaries of a few
microns in diameter to crude oil flow
through an 800 mile long, 4 ft diameter pipe
Explains why airplanes are streamlined
with smooth surfaces
Explains why golf balls are made will
dimpled surfaces for most efficient travel
5
Drag (Pounds of Force)
Effect of Dimples on Golf Balls
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
Drag for Sphere
Drag for Golf Ball
0
100
200
300
400
Velocity (Feet per Second)
6
A List of Some...

...Chapter 3: FLUID FLOW
CHAPTER
THREE
FLUID FLOW
3.1 3.2 3.3 3.4 3.5
Fluid Flow Unit Pump Test Unit Hydraulics bench and accessories Flow Curve Determination for Non-Newtonian Fluids Fixed and Fluidized Bed
Facts which at first seem improbable will, even in scant explanation, drop the cloak which has hidden them and stand forth in naked and simple beauty. GALILEO GALILEI
1
3.1. FLUID FLOW UNIT
Keywords: Pressure loss, straight pipe, pipe bend, orifice meter, venturi meter.
3.1.1. Object
The object of this experiment is to investigate the variations in fluid pressure for flow in straight pipes, throughpipe bends, fittings, orifice and venturi meters.
3.1.2. Theory
When a fluid flows along a pipe, friction between the fluid and the pipe wall causes a loss of energy. This energy loss shows itself as a progressive fall in pressure along the pipe and varies with the rate of the flow. The head loss due to friction can be calculated by the expression:
Lu 2 D
hf 4 f
(3.1.1)
where
hf : head loss due to friction, m H2O D : diameter of pipe, m f : friction factor g : acceleration due to gravity, m/sec2 L : length of pipe, m u : mean velocity, m/sec : density of...

...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 termpipe 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 throughpipes, energy is lost inevitably due to frictions which occur...

...MP4005
1
NANYANG TECHNOLOGICAL UNIVERSITY
SEMESTER 2 EXAMINATION 2012-2013
MP4005 – FLUIDDYNAMICS
April/May 2013 Time Allowed: 2 ½ hours
INSTRUCTIONS
1. This paper contains FOUR (4) questions and comprises FOUR (4) pages.
2. Answer ALL FOUR questions.
3. All questions carry equal marks.
4. This is a CLOSED-BOOK examination.
5. The Compressible Gas Tables comprising of TWELVE (12) pages are enclosed.
1 (a) Derive the area-velocity relationship in compressible flow. Describe briefly the significance of this relationship in subsonic and supersonic regimes.
(6 marks)
(b) Air at M = 0.33 (static pressure 100 kPa and static temperature 300 K) flows isentropically into a converging duct. The inlet area is 0.03 m2.
(i) Determine the exit area where the local Mach number is sonic.
(2 marks)
(ii) Determine the location inside the converging duct where the local Mach number is 0.7.
(2 marks)
(iii) What are the stagnation temperature and stagnation pressure inside the converging duct?
(2 marks)
(c) A divergent duct is now connected to the exit of the convergent duct described in part 1(b) above. The exit area of the divergent duct is 0.04 m2.
(i) What is the maximum mass flow inside the converging-diverging duct if it is choked?
(5 marks)
(ii) Determine the exit static pressure and exit Mach number when a normal shock wave appears
(a) at the exit of the diverging duct, and (4 marks)
(b) in the middle of the diverging duct? (4...

...
Introduction:
In any pipe system there is going to be a loss of energy due to the effect of viscosity from a fluid acting upon the surface of the pipe, this is called Friction Loss. This type of lost depends on the shear stress due to the walls of the pipe and the fluid. It also depends in weather the fluid is laminar or turbulent.
A major difference between these two flows is that due to a viscous layer created in turbulent flow the roughness of the pipe can be taken in account while in laminar flow, it can be neglected because that layer is not created. Many factors are taken in account when we want to measure the energy lost during the trajectory of a fluidthrough a pipe such as, distance, diameter, roughness of the surface, viscosity of the fluid, all affect friction loss. However, many of the aforementioned factors are considered “minor loss,” but friction loss is considered a “major loss.”
The frictional resistance to which a fluid is subjected, as it is moving along a pipe it continuously losses energy going downstream. The mean velocity in the pipe (remains constant) the friction factor f is defined by
And the Reynolds number can be obtained by
For typical flows in smooth pipes, laminar flow corresponds to Re<2300, and the turbulent flow corresponds...

...Flow
Smooth Pipe Law Rough Pipe Law Different Workers Results Application
Energy/ pressure loss problem Velocity/ flow rate problem Pipe Sizing Problem
•
Explicit Equation for Friction Factor
CN2122 / CN2122E
Main Topics
• • •
Equivalent Diameter for Non- Circular Conduit Pressure Drop due to Fittings Loss of Head at Abrupt Enlargement
Exit Loss Loss of Head at abrupt Contraction Entry Loss
Combinations ofPipes
CN2122 / CN2122E
11.0 Introduction
In this chapter, we will go back to consider what we have left out in Chapter 7- viscous work done term. Because of this, this chapter is quite important for it is dealing with real practical problems. For chemical engineers, more than 90% of their problems involve flows in closed conduits.
CN2122 / CN2122E
11.1 Reynolds' Experiment
The classic Reynolds experiment on viscous flow was conducted in 1883. Water is made to flow through a glass pipe as shown in Fig.11.1.1, the velocity being controlled by an outlet valve. At the inlet of the pipe, a dye having the same specific weight as water is injected into the flow. When the outlet valve is only slightly open, the dye will move through the glass pipe intact, forming a thread as illustrated in Fig.11.1.2.a. The orderly nature of this flow is apparent from this demonstration. However, as the valve is...

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