CIVIL ENGINEERING FORMULAS

HYDRAULICS AND WATERWORKS FORMULAS 345

Qdischarge, cfs (cu m/s)

Q 1 discharge at 1 ft head cfs (cu m/s)

tthickness, in, or time, sec

ucircumferential velocity of a point on runner, fps (m/s)

Vabsolute velocity of water, fps (m/s)

Vutangential component of absolute velocity Vcos

Vrcomponent of Vin radial plane

vvelocity of water relative to runner, fps (m/s)

wweight of water per cu ft (cu m)

The theoretical horsepower PTof a hydraulic turbine can be expressed as

(12.162)

The actual horsepower of a hydraulic turbine is the theoretical horsepower
multiplied by the turbine efficiency e,

(12.163)

(12.164)

(12.165)

(12.166)

(12.167)

(12.168)

The laws of proportionality for homologous turbines are:

For constant For constant For variable

runner diam head diam and head

P&H^3 /^2 P&D^2 P&D^2 H^3 /^2

n&H^1 /^2 n&1/Dn&H^1 /^2 D

Q&H^1 /^2 Q&D^2 Q&D^2 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.

eover-all efficiency of turbineehem

nsspecific speednPH5/4n 1 P 1

n 1 rpm at 1 ft headnH

Q 1 discharge at 1 ft headQH, cfs

P 1 horsepower at 1 ft headPH3/2

PePTeHQ8.82

PTHQw 550 HQ8.82

QH,