Download - Intro to fluid flow
Learning Outcomes
After this lecture you should be able to…Explain viscosity and how it changes with temperatureWrite the continuity equationDefine laminar and turbulent flow by using the Reynolds numberDetermine if a flowrate is laminar or turbulentWrite and Explain the Bernoulli equationApply the Bernoulli equation
Basics of Fluid Flow
A fluid is a substance that flowsWhen subjected to a shearing stress layers of the fluid slide relative to each otherBoth gases and liquids are defined as fluidsFluid mechanics is the study of the flow of gases and liquidsThe degree of resistance to shear stress is represented by the term ‘viscosity’High viscosity means high resistance to shear stress – does not flow easily
ViscosityDynamic Viscosity or Viscosity is a measure of resistance to shearing motionThe unit is Ns/m2…….but it has no name!The poise or centipoise is the SI cgs unit1 centipoise = 1 x 10-3 Ns/m2
Typical values for viscosityWater at 20°C = 1 cPAir at 20°C = 1.8 x 10-2 cPCrude Oil = 7.2 cPPetrol = 0.29 cP
You may hear the term ‘kinematic viscosity’This is dynamic viscosity divided by fluid densityIts SI cgs unit is the Stoke (= 1 cm2/s)NB – Viscosity is a function of temperature. For liquids, viscosity decreases as temperature increases
Basics Equations for Fluid Flow
The continuity equation Q = v.awhere v is the velocity (m/s) and a the area available for flow (m2 e.g. cross sectional area of a pipe) and Q is the flowrate (m3/s)The Reynolds number is used to define laminar and turbulent flowLaminar flow is defined by slow moving, uniform, even, smooth flow (e.g. a canal)Turbulent flow is uneven and rough (e.g. a white water river)Bernoulli equation. Daniel Bernoulli lived in the 18th
century and derived a relationship between velocity, height and pressure
The Continuity equation
Q=vaQ – flowrate, m3/sv – fluid velocity, m/sa – area available for flow, m2
What is the flowrate from your kitchen tap?(What is the volume of your kettle and how long does it take to fill it?)The pipe feeding the tap is 15mm. What is the cross sectional area?Use the continuity equation to determine the velocity
Continuity Equation contd.
Imagine a long pipe of varying diameter.The flowrate is constantWhere the diameter is large, the velocity is smallWhere the diameter is small, the velocity is large
d1v1
1 2
d2v2
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Osborne Reynolds 1842 - 1912
A pioneer in Fluid MechanicsHe discovered the nature of flow depends on
VelocityFluid physical propertiesGeometry of the channel/pipe
Sometimes flow is even and smoothSometimes it is uneven and roughHe asked Why?
Reynolds Experiment - Velocity
His first discovery ……At very low water flowrates, dye did not break upImplies no mixing between dye and water!
Dye
Reynolds Experiment - Velocity
….. And at high water flowrates, dye did break upDye mixed with water
Dye
Reynolds Concluded that
At low flowrates we get streamline or laminar flowFlow is characterised by streams that don’t mixAt high flowrates we get turbulent flow and a lot of mixing
Increase Velocity
Further Experiments - Viscosity
Reynolds heated the waterWhen heated the change from laminar to turbulent occurred sooner (at a lower velocity)This is explained by viscosityViscosity decreases as temperature increases
Decrease Viscosity
Further Experiments - Density
Reynolds replaced water with liquids of different densityThe change from laminar to turbulent occurred sooner for high density liquids
Increase Density
Further Experiments – Tube diameter
Reynolds used tubes of different diameterHe discovered that as the diameter increased the change to turbulent occurred sooner
Increase Diameter
Reynolds Number
He combined these observations into a dimensionless number which now carries his name
µρvd
=Re
Re = Reynolds numberρ = density (kg/m3)v = velocity (m/s)d = pipe diameter (m)µ = viscosity (kg/ms)
Activity – Laminar or Turbulent?
Is the flow from your kitchen tap laminar or turbulent?Determine the Reynolds No. and then use the table below
0 < Re <2000 Laminar flow 2000 < Re < 4000 Transition regionRe > 4000 Turbulent flow
Daniel Bernoulli (1700 – 1782)
Bernoulli was a pioneer in Science. His interests were medicine and engineeringBernoulli, with Leonard Euler, investigated the relationship between pressure and velocityThey punctured a pipe with a straw and observed that the height of liquid in the straw is related to the pressure in the pipeThis was used to measure blood pressure where patients arms were punctured with glass capillaries
Conservation of Energy
Bernoulli reasoned that the sum of pressure and kinetic energy is the same for any two points in a pipe
CPv =+2
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ρ
This implies that if the velocity increases, pressure decreases.This is true for a horizontal pipe only.
Bernoulli Equation
Include a term for gravity, ρgh, to get the Bernoulli
Equation as follows
CghPv =++ ρρ 2
21
This is often written as follows:2222
2111 2
121
vghPvghP ρρρρ ++=++
Points 1 and 2 could be at two places in a pipe:
d1v1P1
1 2
d2v2P2
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Activity – Bernoulli Eqn Units
Determine the units of each term in the Bernoulli equation
CghPv =++ ρρ 2
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Bernoulli Eqn Rearranged
Instead of expressing each term in units of Pressure, rearrange to give units of height
Chg
Pg
v=++
ρ2
2
How a chimney works
Point 1 is at the top of the chimney where the velocity is the same as the wind speedPoint 2 is in the fireplace where the velocity is almost zero
Activity – Flow in a pipe
A water mains supply enters a house at ground level (point 1) and rises vertically to the attic tank at an elevation of 10 m (point 2). No change in diamter.What is the ∆P?
10m
Point 2V = 2 m/s
Point 1
Activity – Bernoulli Eqn 2
Same as before except the pipe changes from 40mm diameter to 20mm. What is the ∆P?
10m
Point 220mmV = 2 m/s
Point 140mmV = ? m/s
Litre/s Litre/min m3/hr m3/s Ft3/hr Ft3/min gpm
1 Litre/s 1 60 3.6 0.001 127.1 2.119 15.85
1 litre/min 0.0167 1 0.06 1.66x10-5 2.12 0.035 0.264
1 m3/hr 0.278 16.67 1 0.00028 35.3 0.588 4.438
1 m3/s 1,000 60000 3,600 1 127,133 2,119 15,850
1 Ft3/hr 0.0078 0.472 0.0283 7.87x10-6 1 0.0167 0.124
1 Ft3/min 0.472 28.3 1.699 0.00047 60 1 7.481
Conversion Table