Problem 1. Given the diameter of the pipe and its virtual slope, to find the discharge and velocity of flow. Here d and i are given, and Q and v are required. Find ζ from (1); then v from (2); lastly Q from (3). This case presents no difficulty.

By combining equations (1) and (2), v is obtained directly:—

v = √ (gdi/2ζ) = √ (g/2α) √ [di / {1 + 1/12d}].

(4)

For new pipes√ (g/2α) = 56.72
For incrusted pipes= 40.13

For pipes not less than 1, or more than 4 ft. in diameter, the mean values of ζ are

For new pipes0.00526
For incrusted pipes0.01052.

Using these values we get the very simple expressions—

v = 55.31 √ (di) for new pipes = 39.11 √ (di) for incrusted pipes.

(4a)