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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 detailing the equations for calculating the flow of liquids through pipes.

Identifier  ExFiles\Box 36\1\  scan 017
Date  18th May 1936
  
R.R. 235 A (400 T) (S.C. 539. 18-5-36) G.{Mr Griffiths - Chief Accountant / Mr Gnapp} 1546.

-5-

X.2907L/P - FLOW OF LIQUIDS THROUGH PIPES

The loss of head of a liquid flowing through a pipe is given by the following equation:-
h = f * (l/m) * (v^2 / 2g)

Where h = loss of head in feet (or total energy per lb in ft. - lbs. per lb).
f = Coeff: of liquid friction.
l = Length of pipe in ft.
m = Hydraulic mean radius of pipe = area of cross section (sq.ft) / perimeter (ft).
= A/p ft.
v = mean velocity of flow (ft/sec).
g = 32.19 ft per second per second.

The loss of pressure
= P = hσ where σ is the density of the liquid (lbs per cubic ft).
= fσ * (l/A) * (v^2/2g)

Whence v = sqrt( (2g * A * P) / (fσ * l * p) )

Quantity flowing in cubic feet per second
= Q = vA = sqrt( A^3 / (f*l*p) ) x sqrt( (2g * P) / σ )

and therefore varies as
sqrt( A^3 / p ) other things being the same.
  
  


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