Parallel Piping System - University of Memphis
[Pages:26]Civil Engineering Hydraulics
Pipes in Parallel
Calvin: You know, Hobbes, some days even your lucky rocket ship underpants don't help.
Parallel Pipes
? There are often cases where we find pipes laid in parallel that begin at the same junction and terminate at the same junction
? One of the most common cases is to replace a segment of pipe with two smaller pipes
? This may be a stopgap measure that just seems to remain in place
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Pipes in Parallel
Monday, October 22, 2012
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Parallel Pipes
? If you have had circuits in physics or an electrical engineering class, you may recognize some of the same methods for solution that are used for solving parallel resistances
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Pipes in Parallel
Monday, October 22, 2012
Parallel Pipes
? The fundamentals are also used in solving for water distribution systems through closed loop piping networks
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Pipes in Parallel
Monday, October 22, 2012
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Parallel Pipes
? We will start with the simplest form of a parallel network containing two pipes
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Pipes in Parallel
Monday, October 22, 2012
Parallel Pipes
? The volumetric flow rate approaching point A is known and due to conservation of mass that is the same as the flow exiting at point B
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Pipes in Parallel
Monday, October 22, 2012
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Parallel Pipes
? We usually know the length and cross section area of both of the pipes from A to B and we want to know how much flow is going through each pipe.
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Pipes in Parallel
Monday, October 22, 2012
Parallel Pipes
? Now the view we have of this system is shown from above so all the pipes shown are on the same elevation
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Pipes in Parallel
Monday, October 22, 2012
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Parallel Pipes
? If we neglect minor losses, all the pressure drops along the two pipes from A to B are due to friction losses
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Pipes in Parallel
Monday, October 22, 2012
Parallel Pipes
? The pressure at A is the same for both pipes and the pressure at B is also the same for both pipes
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Pipes in Parallel
Monday, October 22, 2012
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Parallel Pipes
? This means that the pressure drop along both pipes must be the same
p3 = p2
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Pipes in Parallel
Monday, October 22, 2012
Parallel Pipes
? Since both of these pressure drops are due to friction we can replace both of them by the pressure loss due to friction loss terms
p3 = p2 f3L3 v32 = f2L2 v22 D3 2g D2 2g
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Pipes in Parallel
Monday, October 22, 2012
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Parallel Pipes
? The diameter and length of each of the pipes is known but we have unknown friction factors and velocities on each side of the expression
p3 = p2 f3L3 v32 = f2L2 v22 D3 2g D2 2g
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Pipes in Parallel
Monday, October 22, 2012
Parallel Pipes
? Since the friction factor is dependent on the Reynolds number and the Re is a function of the velocity, we have an expression that cannot be solved directly
p3 = p2 f3L3 v32 = f2L2 v22 D3 2g D2 2g
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Pipes in Parallel
Monday, October 22, 2012
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Parallel Pipes
? Most of the solution methods assume a flow in one of the pipes (which sets the flow in the other) and then iterates the solution until the difference in pressure drops is within tolerance.
p3 = p2
f3L3 v32 = f2L2 v22 D3 2g D2 2g
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Pipes in Parallel
Monday, October 22, 2012
Parallel Pipes
f3L3
v32
= f2L2
v
2 2
d3 2g d2 2g
Q32
Q22
f3L3 A32 = f2L2 A22 d3 2g d2 2g
Q32
Q22
f3L3
d32 4
2
=
f2L2
d 4
2 2
2
d3 2g
d2 2g
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Pipes in Parallel
? One method that is used it to manipulate the expression so that we get an equivalent to an electrical circuit
Monday, October 22, 2012
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