(2)
| Fig. 81. |
Suppose pressure columns introduced at A and B. The water will rise in those columns to the heights p1/G and p2/G due to the pressures p1 and p2 at A and B. Hence (z1 + p1/G) − (z2 + p2/G) is the quantity represented in the figure by DE, the fall of level of the pressure columns, or virtual fall of the pipe. If there were no friction in the pipe, then by Bernoulli’s equation there would be no fall of level of the pressure columns, the velocity being the same at A and B. Hence DE or h is the head lost in friction in the distance AB. The quantity DE/AB = h/L is termed the virtual slope of the pipe or virtual fall per foot of length. It is sometimes termed very conveniently the relative fall. It will be denoted by the symbol i.
The quantity Ω/χ which appears in many hydraulic equations is called the hydraulic mean radius of the pipe. It will be denoted by m.
Introducing these values,
ζv2/2g = mh/L = mi.
(3)
For pipes of circular section, and diameter d,
m = Ω/χ = 1⁄4πd2/πd = 1⁄4d.
Then