Bends.—Weisbach traces the loss of head at curved bends to a similar cause to that at elbows, but the coefficients for bends are not very satisfactorily ascertained. Weisbach obtained for the loss of head at a bend in a pipe of circular section
ɧb = ζbv2 / 2g;
(6)
ζb = 0.131 + 1.847 (d/2ρ)7/2,
where d is the diameter of the pipe and ρ the radius of curvature of the bend. The resistance at bends is small and at present very ill determined.
Valves, Cocks and Sluices.—These produce a contraction of the water-stream, similar to that for an abrupt diminution of section already discussed. The loss of head may be taken as before to be
ɧv = ζvv2 / 2g;
(7)
where v is the velocity in the pipe beyond the valve and ζv a coefficient determined by experiment. The following are Weisbach’s results.
Sluice in Pipe of Rectangular Section (fig. 92). Section at sluice = ω1 in pipe = ω.