(4a)
For tubes of uniform section m is constant; for steady motion W is constant; and for isothermal expansion τ is constant. Integrating,
log H + gΩ2p2 / W2cτ + ζ l / m = constant;
(5)
for
l = 0, let H = H0, and p = p0;
and for
l = l, let H = H1, and p = p1.
log (H1/H0) + (gΩ2 / W2cτ) (p12 − p02) + ζ l / m = 0.
(5a)