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Key Concepts: Flow of a
fluid in a pipe can be laminar, transitional, or turbulent. The pipe
is
assumed to be completely filled and
the fluid flowing in the pipe is assumed to be steady,
viscous,
and incompressible. Apply the
principles of conservation of mass (continuity equation)
and
conservation of energy apply to analyze pipe flow.
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In a Nut Shell: Pipe
flow is a common way to transport fluid from one location to another.
Filling
your gas tank, supply of water from a water tower, plumbing in your home, and
transport
of
crude oil in Alaskan pipe lines are
just a few examples.
The
chart below summarizes a few key elements for laminar and turbulent pipe flow.
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Pipe Flow (Single Pipe) |
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Laminar |
Turbulent |
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Linear Shear Stress Distribution
and
Parabolic Velocity Profile
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Pressure Drop proportional to length
∆p/(1/2 ρV2) =
(L/D) φ{Re, ε/D}
Mass flow at each section along
pipe is constant
Energy In + Net Work Rate =
Energy Out + Loss
( between sections ) |
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Shear stress, τ
= 2τw r/D
Velocity
Profile, u( r ) = Vc [ 1 – (2r/D)2 ]
Newtonian model for
shear stress gives
τ = -
μ du/dr
u( r ) =
[τw D / (4μ)] [ 1 –
(r/R)2 ]
Q =
[(πD4)/128 ] ∆P/μL
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Friction
and various fittings in
pipes
results in energy loss.
Major
loss occurs along a length of
pipe
between sections.
Minor
losses occur at elbows, tees,
valves,
bends, etc
Further
discussion follows. |
Click
here to continue discussion. |