Characteristics of Fluid Flows
Chapter 2 Henderson, Perry and
Young
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Laminar and Turbulent Flow
• Laminar: fluid flows in parallel elements,
velocity remains constant but not always
the same as the adjacent element
• Turbulent: fluid moves in elemental swirls
or eddies…velocity and direction of each
element change with time
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Figure 2.2
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• Velocity is highest at the center
• At surface velocity is zero
• Reynolds found 4 factors affecting velocity
– D V ρ and μ so (pipe dia., average V, density
and dynamic viscosity of fluid)
– Re = D V ρ /μ
– Re< 2130….laminar
– Re>4000….turbulent
– 2130<Re<4000….impossible to predict
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exactly
4
• Can be used for other shapes by
calculating the “hydraulic diameter”
• Dh = 4 (area of cross section)/(wetted
perimeter)
• For pipe Dh = 4(πD2/4) / (πD) = D
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Friction Losses
• Darcy
F=f(L/D)V2/2g)
• f is a function of the Re and relative
roughness of the pipe. Table 2.2
• And moody diagram Fig 2.6
• Use either
– For Re < 2130
f = 64/Re
– For Re>2130
f = 0.25/(log10(ε/3.7D)+2.51/(Re f 0.5)))2
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Example 2.4 pg 24
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Friction loss in fittings
• Follows Bernoullis equation…
F = K(V2/2g)
K = friction loss factor
K is empirically determined Table 2-3
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Friction loss in sudden
enlargements in pipe
• F = (V1 – V2)2 / 2g
Fig 2.7
• If expansion is large….velocity 2 becomes
0 and drops from the equation above
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Flow of air through particles
• Fixed bed of granular
material….resistance is a function of
– size,
– shape,
– surface configuration,
– size distribution,
– Method of placement (affects void space)
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Flow of air through particles
• Fixed bed of granular
material….resistance is a function of
– size,
– shape,
– surface configuration,
– size distribution,
– Method of placement (affects void space)
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Flow of air through particles
• Much empirical testing…
– F = Δp/ϒ = f(L/Dp)(V2/2g)
• (specific weight of fluid or air)
– When the particles are not spheres…
• Dp = 6vp/sp
– particle volume and particle surface area
– f = ((1 – εp)/ε3p)(300(1-εp)/(Re + 3.5)
• εp= bed voidage
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Fluid  Air
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Flow of air through particles
• Pressure loss
– Δp/L = a V2/ln(1+bV) for clean loosely packed
material
– a and b are constants…see Table 2-5
– Use 1.5 for packed or dirty material
– After Δp is calculated…
• Bernoullis F = Δp/ϒ
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Flow of air through floors
• Perforated floors or walls that contain
products add energy loss
• Floors: F = (1.071)(V/Of)2 / (ρg) see pg 29-30
• With product on the floor:
– F = (1.071)(V/Ofεp)2 / (ρg) includes
voidage fraction of the material
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Aero/Hydrodynamic Properties
• Air and water are used to remove foreign
material from products
• How much air required depends on the drag
force FD ( sum of skin friction and pressure
drag)
• FD affected by density, abs. viscosity, area and
velocity (equation 10.1)
• Reference Figure 10.1
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Dr. C. L. Jones
Biosystems and Ag. Engineering
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Figure 10.1
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Aero/Hydrodynamic Properties
• FD depends on the drag coefficient CD which is
quantified using the Reynolds number.
• NRe = Vdpρf/η
Where:
»
»
»
»
V = fluid velocity
dp = particle dimension
ρf= fluid density
η = absolute viscosity
• NRe<1.0, Stokes flow, FD=3πdpμV (sphere)
• NRe<1,000 Laminar flow
• NRe >20,000 Turbulent flow
BAE 2023 Physical Properties
Dr. C. L. Jones
Biosystems and Ag. Engineering
18
Aero/Hydrodynamic Properties
• Terminal velocity: occurs when drag force balances
gravitational force
• See Table 10.1
• For a sphere
– Fdrag=CD(πd2/4)(ρfv2/2)
• CD depends on the Reynold number of the particle:
Rep= ρfvd/μ (restated from eqt. 10.1 in different terms)
• If Rep<0.2, CD=24/Rep
• If Rep>200,000, CD=0.44
• If Repis between 500 and 200,000,
CD=(24/Rep)(1.0 + 0.15(Rep)0.687)
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Dr. C. L. Jones
Biosystems and Ag. Engineering
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Lecture 17 – Aero/Hydrodynamic
Properties (Ch. 10)
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Dr. C. L. Jones
Biosystems and Ag. Engineering
20
Aero/Hydrodynamic Properties
Read Example Problem 10.1. You
will need to be familiar with it. This
examples shows how to find a
Reynolds number for a particle, the
drag coefficient and the terminal
velocity
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Dr. C. L. Jones
Biosystems and Ag. Engineering
21
Aero/Hydrodynamic Properties
Application example: Can corn stalks be
separated from corn cobs pneumatically?
What minimum air velocity can be used?
How well will it be separated?
How could we improve the separation?
BAE 2023 Physical Properties
Dr. C. L. Jones
Biosystems and Ag. Engineering
22
Aero/Hydrodynamic Properties
Application example: A seed company would
like to move soybeans through a pipe (5.25”
inside diameter) pneumatically. What capacity
should the air source (the fan) be rated for?
BAE 2023 Physical Properties
Dr. C. L. Jones
Biosystems and Ag. Engineering
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