Page 309 - Fair, Geyer, and Okun's Water and wastewater engineering : water supply and wastewater removal

JWCL344_ch08_265-296.qxd 8/2/10 9:53 PM Page 269

8.2 Pump Characteristics 269
Changing the speed of a centrifugal pump will also change its power requirement. If
the speed of a pump (rpm) is changed, its head will change as follows:
P (P )(N >N ) 3 (8.4)
2
1
1
2
where
P 2 power requirement now, hp (kW)
P 1 rated power requirement, hp (kW)
N 2 pump speed now, rpm
N 1 rated pump speed, rpm.

EXAMPLE 8.1 DETERMINATION OF PUMP NEW POWER REQUIREMENT
Changing the speed of a centrifugal pump will change its operating characteristics, including the
power requirement.
Determine the new power requirement, if

P 1 rated head 20 hp 14.914 kW
N 2 pump speed now 1,200 rpm
N 1 rated pump speed 1,425 rpm

Solution 1 (U.S. Customary System):
P 2 (P 1 )(N 2 >N 1 ) 3
3
(20 hp)(1,200>1,425) 12 hp

Solution 2 (SI System):
P 2 (P 1 )(N 2 >N 1 ) 3
3
(14.914 kW)(1,200/1425) 8.948 kW

8.2.1 Power Requirements and Efficiencies of Pumps
Work can be expressed as lifting a weight a certain vertical distance. It is usually defined in
terms of ft-lb of work. Power is work per unit of time. These statements are expressed
mathematically by the following relationships:

Work WH (8.5)
Power Work/t (8.6)
where
Work work, ft-lb (m-kg)
W weight, lb (kg)
H height, ft (m)
Power power, ft-lb/s (m-kg/s)
t time, s.
If the water flow from a pump is converted to weight of water and multiplied by the
vertical distance it is lifted, the amount of work or power done can be represented by the
following equation:
Power Work/t WH/t
HP (Q, gpm)(8.34 lb/gal)(H, ft)(min/60 s)(horsepower/550 ft-lb/s)
HP (Q)(H)>3,957 (8.7)