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Flow of Water in Pipes Equations and Calculator

Fluids Design and Engineering Analysis

Flow of Water in Pipes Equations and Calculator

The volume of water that flows through a pipe depends on the head (pressure) but also on the diameter of the pipe, the character of the interior surface, and the number and shape of the bends. The head may be either the distance between the levels of the surface of water in a reservoir and the point of discharge, or it may be caused by mechanically applied pressure, as by pumping, when the head is calculated as the vertical distance corresponding to the pressure.

One pound per square inch is equal to 2.309 feet head, and a 1-foot head is equal to a pressure of 0.433 pound per square inch.

All formulas for finding the amount of water that will flow through a pipe in a given time are approximate. The formula that follows will give results within 5 or 10 per cent of actual flows, if applied to pipe lines carefully laid and in fair condition.

V_fps = V · 0.7854
L_e = [ ( 4 d ) / 3 ] n (See note at bottom)

Where:

V = approximate mean velocity in feet per second
V_fps = approximate mean volume in cubic per second
C = coefficient from the accompanying table
D = diameter of pipe in feet;
h = total head in feet;
L = total length of pipe line in feet + L_e
L_e = Equivalent length right angle bend in ft
n = Number of right angle bends

Coefficient C
( Extrapolate C where Required )

Dia. of Pipe		C
Feet	Inches
0.1	1.2	23
0.2	2.4	30
0.3	3.6	34
0.4	4.8	37
0.5	6.0	39
0.6	7.2	42
0.7	8.4	44
0.8	9.6	46
0.9	10.8	47
1.0	12.0	48
1.5	18.0	53
2.0	24.0	57
2.5	30.0	60
3.0	36.0	62
3.5	42	64
4.0	48	66
5.0	60	68
6.0	72	70
7.0	84	72
8.0	96	74
10.0	120	77

Note:

The loss of head due to a bend in the pipe is most frequently given as the equivalent length of straight pipe, which would cause the same loss in head as the bend. Experiments show that a right-angle bend should have a radius of about three times the diameter of the pipe. Assuming this curvature, then, if d is the diameter of the pipe in inches and L is the length of straight pipe in feet that causes the same loss of head as the bend in the pipe, the following formula gives the equivalent length of straight pipe that should be added to simulate a right-angle bend.

L = ( 4 d ) / 3

Reference: Machinerys Handbook, 27th Edition