Let p0, p1, p2 be the pressures at the three sections. Applying Bernoulli’s theorem to the sections A0A0 and A1A1,
| p0 | + | v2 | = | p1 | + | v12 | . |
| G | 2g | G | 2g |
Also, for the sections A1A1 and A2A2, allowing that the head due to the relative velocity v1 − v is lost in shock:—
| p1 | + | v12 | = | p2 | + | v2 | + | (v1 − v)2 | ; |
| G | 2g | G | 2g | 2g |
∴ p0 − p2 = G (v1 − v)2 / 2g;
(2)
or, introducing the value in (1),
| p0 − p2 = | G | ( | Ω | − 1 ) | 2 | v2 |
| 2g | cc (Ω − ω) |
(3)
Now the external forces in the direction of motion acting on the mass A0A0A2A2 are the pressures p0Ω1 − p2Ω at the ends, and the reaction −R of the plane on the water, which is equal and opposite to the pressure of the water on the plane. As these are in equilibrium,