Page 421 - Civil Engineering Formulas

HYDRAULICS AND WATERWORKS FORMULAS 347

h aV {g[N K(N 1)]} for K 1, N 1 (12.176)

h aV [g(2N K)] for K 1, N 1 (12.177)
where K aV (2gH); N aT (2L). V and H are the penstock velocity, ft/s (m/s);
and head, ft (m), prior to closure; L is the penstock length, ft (m); and T is the
time of gate closure. For full load rejection, T may be taken as 85 percent of the
total gate traversing time to allow for nonuniform gate motion.
For pressure drop following a complete gate opening, the following formula
(S. Logan Kerr) may be used with T not less than 2L/a:
2
aV K K N 2
h pressure drop, ft (m) (12.178)
g N 2
Speed Rise Following Load Reduction.* For sudden load reductions in the
electrical system that a hydraulic turbine serves, the approximate speed rise is

2 2 1 2
3 2
n t n [1 1,620,000T t P t (1 h H) WR n ] (USCS) (12.179)
3 2
2 2 1 2
[1 365,000T t P t (1 h H) GD n ] (SI)
where n is the speed, rpm, at the end of time T ; n is the speed, rpm, before the
t
t
load decrease; T is the time interval, seconds, for the governor to adjust the flow
t
to the new load; P is the reduction in load, hp (kW); h is the head rise caused by
t
the retardation of the flow, ft (m); H is the net effective head before the load
2
change, ft (m); WR is the product of the revolving parts weight, lb, and the
2
square of their radius of gyration, ft; and GD is the product of the revolving
parts weight, kg, and the square of their diameter of gyration, m.
Speed Drop Following Load Increase. For sudden load increases in the
electrical system that a hydraulic turbine serves, the approximate speed drop is
3 2 1 2
2 2
n t n [1 1,620,000T t P t WR n (1 h H) ] (USCS) (12.180)
3 2 1 2
2 2
[1 365,000T t P t GD n (1 h H) ] (SI)
where P is the actual load increase and h is the head drop caused by the
t
increase of the flow. If the speed drop is to be determined for a given increase
in gate opening, the governor time T for making this increase and the normal
t
change in load for the change in gate opening, under constant head H, can be
used in the following formula:
2 2 1 2
3 2
n t n [1 1,620,000T t P t (1 h H) WR n ] (USCS) (12.181)
3 2
2 2 1 2
[1 365,000T t P t (1 h H) GD n ] (SI)
3 2
The actual change in load, however, will be P t (1 h H) .
*Marks—Mechanical Engineer’s Handbook, McGraw-Hill.