1. Reading Materials: Chapter 6
Fluid Flow
LECTURES 16-18
CHEM ENG 1007

2. What is a Fluid Material that continually deforms under a shear stress
Divided into two groups
Liquid
Gases
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3. GASES
Characterized as loosely-associated molecules which are normally not close together and which travel through space for long distances before colliding with each other. The velocity of their travel depends on the temperature of the gas.
Characteristic of gases:
Readily compressible
Expand quickly and fill a container
To convert from volume to mass/mole use
PV=nRT
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4. LIQUIDS Density = mass/volume
Characterized by molecules which are very close together and which are in collision with each other very frequently as they move around each other. The velocity of that motion and the rate of that collision depend on the temperature of the liquid.
Characteristic of liquids:
Slightly compressible
Takes shape of container sides and bottom
To convert from volume to mass/mole use
Density = mass/volume
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5. Fluid-Like Systems Solids present in fluids Slurries
fine particles suspended in liquid
Solids in a fluidized bed
particles moving with the fluid in a tall reactor.
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6. Variables associated with fluids
Others
Thermal conductivity
Electrical conductivity
Boiling point
Freezing point
Heat capacity
Enthalpy
Density
Flow rate
Pressure
Viscosity
Surface tension
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7. Flow Rate
Rate at which a material is transported through a process line.
Mass flow rate:
Molar flow rate:
Volume flow rate:
where:
Chapter 7
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8. Pressure
The pressure of the fluid is defined as the total force (exerted on the boundary by the fluid molecules) divided by the surface area of the boundary it is acting upon.
{F}
{A}
{P} SI N m2
Nm-2 (Pa)
cgs
dyne
cm2
dynecm-2
American
lbf
in2
lbfin-2 (psi)
Chapter 7
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9. Puzzle Pressure = force/area
A woman’s high heels sink into the soft ground, but the larger shoes of the much bigger man do not.
Pressure = force/area
Chapter 7
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10. Pressure We express pressure in two ways: absolute and gauge pressures
Gauge Pressure: fluid pressure that is measured relative to the atmospheric pressure.
Absolute Pressure: the total magnitude of force exerted per unit area
In process calculations:
Pabs = Pgauge + Patmosphere
Pabs = 0 in complete vacuum
Letter “a” or “g” is added to designate absolute or gauge, thus psia or psig
Chapter 7
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11. Standard Atmospheric Pressure
At sea level, 0oC and 45o latitude:
Patm = 1 atm
= 101,325 Pa
= 14.7 psi
= bars
= 760 mmHg
= m H2O = ft H2O
Chapter 7
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12. Standard Atmospheric Pressure
How much does the atmosphere heigh?
Answer: the same as 76 cm of mercury. How?
Torricelli filled a tube with mercury and inverted it into an open container of mercury. Air pressure acting on the mercury in the dish can support a column of mercury 76 cm in height.
Chapter 7
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13. Example 7.1
A man pumps his automobile tire until the tire gauge reads 34.0 psi. If the atmosphere in his community is 14.2 psia, what is the absolute pressure of the air in the tire?
Solution:
Pg = 34.0 psig
Patm = 14.2 psia
Pabs = = 48.2 psia
Chapter 7
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14. Hydrostatic Pressure
It is the pressure (P) of the fluid at the base of the column. That is the force (F) exerted on the base divided by the base area (A). F thus equals the force on the top surface plus the weight of the fluid in the column.
P = P0+ gh
h = height of a hypothetical column of the
fluid
A pressure may also be expressed
as a head of a particular fluid (Ph)
Ph = P0 + h
Chapter 7
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15. Example 7.2
For the tank depicted in Fig. 7.2, if the NaOH solution is 8 ft high, what is the pressure at the bottom of the tank? Assume that the density of the NaOH solution is the same as that of water. Perform the calculation in metric units.
Solution:
P1 = 0 Pa (gauge), so P2 = 23,896 Pa (gauge)
or P2 = 23, ,325 = 125,221 Pa (absolute)
Chapter 7
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16. Quick Quiz 1
What is the pressure 30.0 m below the surface of a lake? Assume the atmospheric pressure (the pressure at the surface) is 10.4 m H2O? Express your answer in atm.
Solution:
Ph = P0 + h
= = 40.4 m H2O
Chapter 7
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17. Fluid Pressure Measurement
A hollow tube closed at one end and bent into a C configuration. The open end of the tube is exposed to the fluid whose pressure is to be measured. As the pressure increases, the tube tends to straighten, causing a pointer attached to the tube to rotate.
Figure (p. 57) of Felder and Rousseau Bourdon gauge. It is used to measured fluid pressure from nearly perfect vacuums to about 7000 atm.
Chapter 7
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18. Fluid Pressure Measurement
Gauge pressure
Pressure difference
Absolute pressure
Figure (p. 58) Manometers. It is used for more accurate measurements of pressure (below about 3 atm)
Chapter 7
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19. Figure 3.4-5 (p. 58) Differential Manometer variables.
Fluid Pressure Measurement
If  is gas then  may be neglected
Figure (p. 58) Differential Manometer variables.
Chapter 7
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20. Illustration 1
A manometer reading gives 100 mmHg, calculate the absolute pressure.
Solution:
Measured gauge pressure:
Pabs = 13, ,325 = 114,653 Pa
= 115 kPa
Chapter 7
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21. How does pressure relate to flow?
In the absence of other forces, fluids tend to flow from regions of high pressure to regions where the pressure is lower. Therefore, pressure differences provide a driving force for fluid flow.
Example: when a tire is punctured, air flows out of the high pressure tire to the atmosphere, which is a low pressure.
Chapter 7
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22. Viscosity (m) Characterises its resistance to flow
A measure of “stickiness” of a fluid
A “frictional force”
Low viscosity fluid
High viscosity fluid
Less energy required for mixing
More energy required for mixing
Chapter 7
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23. Viscosity (m) Measurement - “Shear stress/shear rate” Units
SI: kg/(m.s) = N.s/m2 = Pa.s
cgs: cp (centipoise)
1 cP = 10-2 poise = 10-3 Pa.s = 1 mPa.s
Chapter 7
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24. Viscosity of various fluids
Temperature (oC)
Viscosity
Pa.s
Water
15.6
1.1x10-3
Gasoline
0.3x10-3
SAE 30 oil
383x10-3
Air 15
1.8x10-5
Methane 20
1.1x10-5
Chapter 7
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25. Viscosity of various fluids
Substance (25°C) Viscosity (Pa.s)
Water x 10-3
Mercury x 10-3
Air x 10-5
Castor oil
Chapter 7
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26. Kinematic viscosity
The property viscosity may also be combined with the fluid’s density to give the property kinematic viscosity
Chapter 7
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27. Types of viscous fluids
Chapter 7
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28. Types of viscous fluids
Newtonian fluid
e.g. water, air, other gases.
2-4 Non-Newtonian fluids
Bingham-plastic.
e.g. toothpaste, margarine, soap
Pseudo-plastic (shear thinning)
e.g. mayonnaise, polymer melts, paints.
Dilatant (shear thickening)
e.g. wet beach sand, starch in water
Chapter 7
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29. Newtonian fluids Question:
How would you determine the viscosity from a plot of shear stress against shear rate?
With Newtonian fluids, shear stress increases proportionately with the shear rate
Shear rate
Shear stress
Shear rate
Viscosity
Examples
Water
Glycerine
Alcohol
Air
Chapter 7
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30. Other types of Non-Newtonian fluids
Dilatant
Pseudoplastic
Shear rate
Viscosity
Viscosity
Shear rate
Viscosity changes with power input
Chapter 7
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31. Other types of Non-Newtonian fluids
Thixotropic
Rheopetic
Viscosity
Viscosity
Time
Time
Viscosity changes with time at constant shear rate
Chapter 7
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32. Non-Newtonian fluids can have more than one property
Example:
Damp gypsum
Pseudoplastic, Thixotropic and Viscoelastic
Cream
Dilatant, Rheopectic and not Viscoelastic
Viscoelastic: Fluid returns to original viscosity after power input ceases
Chapter 7
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33. Ideal / Inviscid Fluid
Hypothetical fluid which is incompressible and has zero viscosity.
Chapter 7
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34. Fluid Flow Principles Flow patterns vary with: velocity
geometry of surface, and
fluid properties such as viscosity, density.
Classic experiment by Osborne Reynolds (1883) observed two types of fluid flow:
Laminar flow – low flow rates
Turbulent flow – higher flow rates
Chapter 7
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35. Reynolds’ experiment
(i) Low flow rates: fluid moves in parallel layers.
(ii) High flow rates: cross currents (eddies) develop
Chapter 7
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36. Reynolds Number Reynolds’ key variables
Arrange into single “dimensionless group”:
Chapter 7
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37. Reynolds Number For pipe flow: Re < 2,100 - laminar flow
2,100 < Re < 10,000 - transition region
Re > 10, turbulent flow
Pipe-flow systems with the same Re are said to be dynamically similar.
Chapter 7
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38. Fluid flow through a pipe
Illustration 2
Fluid flow through a pipe
Water at 25oC flows through a pipe of internal diameter 0.1 m at a velocity 0.2 m/s.
Is the flow laminar flow or turbulent?
What is the effect of reducing the velocity by a factor of 10?
Chapter 7
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39. Solution
Chapter 7
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40. Velocity Profiles: Laminar Flow
Velocity profile is parabolic with the maximum velocity occurring in the centre of the pipe (r = 0)
(i) Laminar Flow
Chapter 7
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41. Velocity Profiles: Laminar Flow
(i) Velocities of a fluid in laminar flow through a circular pipe
Chapter 7
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42. Velocity Profiles: Laminar Flow
Volumetric flow rate:
Mean velocity:
Chapter 7
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43. Velocity Profiles: Turbulent Flow
Difficult to mathematically model due to its complex and rapidly changing flow patterns.
Experimental measurements show for time-averaged velocity and mean velocity
(ii) Turbulent Flow
Chapter 7
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44. Velocity Profiles: Plug Flow
Common assumption for highly turbulent flow is that velocity does not vary over cross-section:
(iii) Plug Flow
Chapter 7
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45. Mass Conservation in Fluid Flow
Consider steady-state, one-dimensional fluid through pipe
Chapter 7
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46. Mass Conservation in Fluid Flow
Is v2 in (a) less than v2 in (b)?
No, they are both the same.
Chapter 7
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47. Fluid Friction
Frictional force cause pressure drop during fluid flow through a constant diameter horizontal pipe.
Consider flow situation in pipe below.
Chapter 7
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48. Fluid Friction Momentum balance:
f = friction factor; L = length of pipe;
D = diameter of pipe;
Chapter 7
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49. Fluid Friction
Chapter 7
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50. Example 7.7
What value of the friction per mass of fluid (ef) is necessary to cause a decrease in pressure equal to
10 psi (answer in Btu/lbm)?
Chapter 7
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51. Example 7.7
What value of the friction per mass of fluid (ef) is necessary to cause a decrease in pressure equal to
b) 68,900 Pa (answer in J/kg)?
Chapter 7
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52. Laminar Flow f determined analytically from velocity profile.
Experimental data confirmed for Re < 2,100 (see Figure )
Chapter 7
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53. Figure 2.10-3: Friction Factor Chart
Chapter 7
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54. Turbulent Flow f cannot be determined analytically.
Experimental curves have been devised.
f also depends on surface roughness factor, e
Pipe
e (mm)
Concrete
Cast iron
0.26
Galvanized iron
0.15
Plastic
0.0 (smooth)
Chapter 7
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55. Turbulent Flow For smooth pipe & 2,100 < Re < 105
Blassius equation may be used:
Chapter 7
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56. Illustration 3 Frictional losses in a pipe
Pipeline 5 km long & 30 cm internal diameter
Conveys water at 25oC at a rate of 180 kg/s.
Roughness factor e/D = 0.001
Estimate the pressure drop across the pipe due to friction.
Chapter 7
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57. Solution
For water
Chapter 7
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58. Solution
From Figure , f = 0.005
Hence,
Chapter 7
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59. Chapter 7
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