Page 419 - Civil Engineering Formulas

HYDRAULICS AND WATERWORKS FORMULAS 345

Q discharge, cfs (cu m/s)
Q discharge at 1 ft head Q H, cfs (cu m/s)
1
t thickness, in, or time, sec
u circumferential velocity of a point on runner, fps (m/s)
V absolute velocity of water, fps (m/s)
V tangential component of absolute velocity V cos
u
V component of V in radial plane
r
v velocity of water relative to runner, fps (m/s)
w weight of water per cu ft (cu m)
The theoretical horsepower P of a hydraulic turbine can be expressed as
T
P T HQw 550 HQ 8.82 (12.162)

The actual horsepower of a hydraulic turbine is the theoretical horsepower
multiplied by the turbine efficiency e,
P eP T eHQ 8.82 (12.163)

P 1 horsepower at 1 ft head P H 3/2 (12.164)
Q 1 discharge at 1 ft head Q H, cfs (12.165)
n 1 rpm at 1 ft head n H (12.166)
n s specific speed n P H 5/4 n 1 P 1 (12.167)
(12.168)
e over-all efficiency of turbine e h e m

The laws of proportionality for homologous turbines are:

For constant For constant For variable
runner diam head diam and head
2
P & H 3 /2 P & D 2 P & D H 3 /2
1 /2
n & H 1 /2 n & 1/D n & H D
2
Q & H 1 /2 Q & D 2 Q & D H 1 /2

Selecting the Turbine Rotative Speed
The speed should be as high as practicable as higher the speed the less
expensive will be the turbine and generator and the more efficient will be the
generator.