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
h1 - h2 = (v1² - v2²)/2g - (v1 - v2)²/2g = v2(v1 - v2)/g (2)
[Illustration: 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
Mt = (W/g)(v2p2 - v1p1),
or, if the change of momentum is estimated for one second,