where p0 is the greater pressure and p1 the less, and the flow is from A0 towards A1.
By replacing W and H,
log (p0/p1) + (gcτ / u02p02) (p12 − p02 + ζ l/m = 0
(6)
Hence the initial velocity in the pipe is
u0 = √ [{gcτ (p02 − p12)} / {p02 (ζ l/m + log (p0 / p1) }].
(7)
When l is great, log p0/p1 is comparatively small, and then
u0 = √ [ (gcτm/ζ l) {(p02 − p12) / p02} ],
(7a)