Within the limits stated, these are accurate enough for practical purposes, especially as the precise value of the coefficient ζ cannot be known for each special case.
Problem 2. Given the diameter of a pipe and the velocity of flow, to find the virtual slope and discharge. The discharge is given by (3); the proper value of ζ by (1); and the virtual slope by (2). This also presents no special difficulty.
Problem 3. Given the diameter of the pipe and the discharge, to find the virtual slope and velocity. Find v from (3); ζ from (1); lastly i from (2). If we combine (1) and (2) we get
i = ζ (v2/2g) (4/d) = 2a {1 + 1/12d} v2/gd;
(5)
and, taking the mean values of ζ for pipes from 1 to 4 ft. diameter, given above, the approximate formulae are
| i = 0.0003268 v2/d for new pipes = 0.0006536 v2/d for incrusted pipes. |
(5a)
Problem 4. Given the virtual slope and the velocity, to find the diameter of the pipe and the discharge. The diameter is obtained from equations (2) and (1), which give the quadratic expression
d2 − d (2αv2/gi) − αv2/6gi = 0.