Hence, equating impulse and change of momentum,
G (h0Ω0 − h1Ω1) t = (G/g) (Ω1u12 − Ω0u02) t;
∴ h0Ω0 − h1Ω1 = (Ω1u12 − Ω0u02) / g.
(1)
For simplicity let the section be rectangular, of breadth B and depths H0 and H1, at the two cross sections considered; then h0 = 1⁄2H0, and h1 = 1⁄2H1. Hence
H02 − H12 = (2/g) (H1u12 − H0u02).
But, since Ω0u0 = Ω1u1, we have
u12 = u02H02 / H12,
H02 − H12 = (2u02/g) (H02/H1 − H0).
(2)