If the flow is horizontal, z2 = z1; and
h1 − h2 = (v22 − v12) / 2g. (la)
(b) When there is an abrupt change of section of the passage, or an abrupt change of section of the stream due to a contraction, then, in applying Bernoulli’s equation allowance must be made for the loss of head in shock (§ 36). Let v1, v2 be the velocities before and after the abrupt change, then a stream of velocity v1 impinges on a stream at a velocity v2, and the relative velocity is v1 − v2. The head lost is (v1 − v2)2/2g. Then equation (1a) becomes
h2 − h1 = (v12 − v22) / 2g − (v1 − v2)2 / 2g = v2 (v1 − v2) / g
(2)
| Fig. 184. |
To diminish as much as possible the loss of energy from irregular eddying motions, the change of section in the turbine passages must be very gradual, and the curvature without discontinuity.
(c) Equality of Angular Impulse and Change of Angular Momentum.—Suppose that a couple, the moment of which is M, acts on a body of weight W for t seconds, during which it moves from A1 to A2 (fig. 184). Let v1 be the velocity of the body at A1, v2 its velocity at A2, and let p1, p2 be the perpendiculars from C on v1 and v2. Then Mt is termed the angular impulse of the couple, and the quantity
(W/g) (v2p2 − v1p1)
is the change of angular momentum relatively to C. Then, from the equality of angular impulse and change of angular momentum