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From the Rolls-Royce experimental archive: a quarter of a million communications from Rolls-Royce, 1906 to 1960's. Documents from the Sir Henry Royce Memorial Foundation (SHRMF).
Page of fluid dynamics calculations for flow in circular pipes, including Darcy's formulas.

Identifier  ExFiles\Box 36\1\  scan 018
Date  16th February 1916
  
-6-
Contd.

If the pipe be of circular cross sectional area.

A = (π/4) * d^2
p = π * d
m = d/4
h = (4fl/d) * (v^2/2g)

and Q = (π/8) * sqrt(d^5/fl) * sqrt(2g * P/σ)

Q therefore varies as d^(5/2) other things being the same.

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A suitable value of f based upon the results of experiments must be chosen for each particular case.

f varies from .005 (1 + 1/(12d)) for new clean pipes
to .010 (1 + 1/(12d)) for old incrusted pipes.

where d = dia. of bore of pipe in feet. (Darcy).

Tables of values of f, suited to particular cases are to be found in books on Hydraulics.

"Unwin's Treatise on Hydraulics" published by Black gives a useful set of tables.

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