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parallel duct or pipe flows

parallel duct or pipe flows

parallel duct or pipe flows

(OP)
fvincent previously quoted a formula for the equivalent resistance of parallel pipe flows.  Where can I find a reference that develops the equation that he gave?  For three pipes it was:

Keq = k1*k2*k3 / ((k2*k3)^.5 + (k1*k3)^.5 + (k2*k3)^.5)^2

RE: parallel duct or pipe flows

(OP)
Thank you athomas236.  The solution was very nice.  My problem is slightly different, however.  I have three parallel flows that do not reconnect, but each discharges to a different pressure.  Can you help with this.  I have used the concept of equivalent resistance with the steady-state energy equation to compute the flow rate but have not sorted out how to calculate/iterate the three exhaust flows. I was assuming that the total pressure loss in each exhaust leg, including the exit pressure, would be the same but so far have not found a solution.

Thanks.

RE: parallel duct or pipe flows

That's NOT parallel flow, its BRANCH flow.. in 3 branches.  Flow will be different in each branch; the flow can be found from each branche's (probably all different) differential pressure (its inlet pressure - outlet pressure).  It sounds like the inlet pressure is common to all branches, which must be greater than all the outlet pressures, or you will get some flow in the reverse direction in any branch where that condition is not happening.   

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