Handbook of Civil Engineering Calculations

PART 3

CENTRIFUGALPUMPS

AND HYDRO POWER

MINIMUM SAFE FLOW FOR A

CENTRIFUGAL PUMP

A centrifugal pump handles 22O
0
F (104.4
0
C) water and has a shutoff head (with closed
discharge valve) of 3200 ft (975.4 m). At shutoff, the pump efficiency is 17 percent and
the input brake horsepower is 210 (156.7 kW). What is the minimum safe flow through
this pump to prevent overheating at shutoff? Determine the minimum safe flow if the
NPSH is 18.8 ft (5.7 m) of water and the liquid specific gravity is 0.995. If the pump con-
tains 500 Ib (225 kg) of water, determine the rate of the temperature rise at shutoff.

Calculation Procedure:

1. Compute the temperature rise in the pump
   With the discharge valve closed, the power input to the pump is converted to heat in the cas-
   ing and causes the liquid temperature to rise. The temperature rise t = (I - e) x H 8 IIlSe,
   where t = temperature rise during shutoff,
   0
   F; e = pump efficiency, expressed as a decimal;
   H 3 = shutoff head, ft. For this pump, t = (1 - 0.17)(3200)/[7780(0.17)] = 20.4
   0
   F (36.7
   0
   C).


2. Compute the minimum safe liquid flow
   For general-service pumps, the minimum safe flow M gal/min = 6.0(bhp input at shut-
   off)/*. Or, M= 6.0(210)720.4 = 62.7 gal/min (3.96 L/s). This equation includes a 20 per-
   cent safety factor.
   Centrifugal pumps usually have a maximum allowable temperature rise of 150 F
   (27^0 C). The minimum allowable flow through the pump to prevent the water temperature
   from rising more than 150 F (27^0 C) is 30 gal/min (1.89 L/s) for each 110-bhp (74.6-kW)
   input at shutoff.


3. Compute the temperature rise for the operating NPSH
   An NPSH of 18.8 ft (5.73 m) is equivalent to a pressure of 18.8(0.433)(0.995) = 7.78
   lb/in^2 (abs) (53.6 kPa) at 22O^0 F (104.4^0 C), where the factor 0.433 converts ft of water to
   lb/in^2. At 22O^0 F (104.4^0 C), the vapor pressure of the water is 17.19 lb/in^2 (abs) (118.5
   kPa), from the steam tables. Thus, the total vapor pressure the water can develop before
   flashing occurs = NPSH pressure + vapor pressure at operating temperature = 7.78 +
   17.19 = 24.97 lb/in^2 (abs) (172.1 kPa). Enter the steam tables at this pressure, and read the
   corresponding temperature as 24O^0 F (115.6^0 C). The allowable temperature rise of the wa-
   ter is then 240 - 220 = 2O^0 F (36.O^0 C). Using the safe-flow relation of step 2, we find the
   minimum safe flow is 62.9 gal/min (3.97 L/s).


4. Compute the rate of temperature rise
   In any centrifugal pump, the rate of temperature rise tr °F/min = 42.4(bhp input at shut-
   off)/wc, where w = weight of liquid in the pump, Ib; c = specific heat of the liquid in the
   pump, Btu/(lb-°F). For this pump containing 500 Ib (225 kg) of water with a specific heat,
   c = 1.0, tr = 42.4(210)/[500(1.0)] = 17.8°F/min (32°C/min). This is a very rapid tempera-
   ture rise and could lead to overheating in a few minutes.