CIVIL ENGINEERING FORMULAS

HYDRAULICS AND WATERWORKS FORMULAS 347

for (12.176)

for (12.177)

where VandHare the penstock velocity, ft/s (m/s);
and head, ft (m), prior to closure; Lis the penstock length, ft (m); and Tis the
time of gate closure. For full load rejection, Tmay 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 Tnot less than 2L/a:

ft (m) (12.178)

Speed Rise Following Load Reduction.* For sudden load reductions in the
electrical system that a hydraulic turbine serves, the approximate speed rise is

(USCS) (12.179)

(SI)

wherentis the speed, rpm, at the end of time Tt;nis the speed, rpm, before the
load decrease; Ttis the time interval, seconds, for the governor to adjust the flow
to the new load; Ptis the reduction in load, hp (kW); his the head rise caused by
the retardation of the flow, ft (m); His the net effective head before the load
change, ft (m); WR^2 is the product of the revolving parts weight, lb, and the
square of their radius of gyration, ft; and GD^2 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

(USCS) (12.180)

(SI)

wherePtis the actual load increase and his the head drop caused by the
increase of the flow. If the speed drop is to be determined for a given increase
in gate opening, the governor time Ttfor making this increase and the normal
change in load for the change in gate opening, under constant head H, can be
used in the following formula:

(USCS) (12.181)

(SI)

The actual change in load, however, will be Pt(1hH)^3 ^2.

[1365,000TtPt(1hH)^3 ^2 GD^2 n^2 ]^1 ^2

ntn[11,620,000TtPt(1hH)^3 ^2 WR^2 n^2 ]^1 ^2

[1365,000TtPtGD^2 n^2 (1hH)^3 ^2 ]^1 ^2

ntn[11,620,000TtPtWR^2 n^2 (1hH)^3 ^2 ]^1 ^2

[1365,000TtPt(1hH)^3 ^2 GD^2 n^2 ]^1 ^2

ntn[11,620,000TtPt(1hH)^3 ^2 WR^2 n^2 ]^1 ^2

h

aV

g

KK^2 N^2

N^2 

pressure drop,

KaV(2gH);NaT(2L).

haV[g(2NK)] K 1,N    1

haV{g[NK(N1)]} K1,N    1

*Marks—Mechanical Engineer’s Handbook, McGraw-Hill.