Temperature rise of liquid at shut-off operation

The rate of temperature rise of a liquid in a casing when a pump operate with fully
closed discharge control valve can be calculated from:

Tr = [ (42.4 x HP) / (W x C) ]

where:

Tr  = rate of temperature rise, deg F/min
HP= BHP at shut-off
W = weight of liquid in pump case, lbs
C  = specific heat of liquid; use 1.0 for water, 0.5 for hydrocarbons if exact value is
unknown

This equation neglects the heat loss through the pump case so its result is
conservative. The weight of liquid can be calculated by estimating the case
volume or requesting for the case volume data from the pump manufacturer;
some manufacturers collect this data from hydrotest or from hydraulic drawings.

Based on the above rate of temperature rise the duration of safe operation at
shut-off can then be calculated by dividing the allowable temperature rise with the
rate of temperature rise.

Rule-of-Thumb: For safe operation the allowable temperature rise should be
limited to 50 degrees F maximum. A lower value of allowable temperature rise
should be considered if the 50 degree limit would result in exceeding the case
design temperature, or to an increase in vapor pressure that could result in critical
NPSH or to potentially damaging vaporization at mechanical seal face.

Example: For how long can a multi-stage pump be operated safely with the
discharge valve closed if the pump required 500 BHP at shut-off and the pump
case contained 200 lbs of water?

Solution: Calculate the rate of temperature rise

Tr = [(42.4 x 500)/(200x1)] = 106 degree/min

Calculate time required to limit temperature rise to 50 degrees F

T = 50/106 = 0.47 minute or 28 seconds

Q  -  We have a four-stage vertical turbine pump, 3050 HP, 720 RPM, 240 FT head
(75 PSIG), with 80 feet shaft length. We want to know its maximum safe operating
time with the discharge valve closed. The operator feel it is safe to run the unit for
five minutes but during this time the pump and motor experienced high vibration.

A  -  It is not unusual for a pump to have an increase in noise and vibration when
operating with the discharge valve closed. Based on the limited information given,
this pump is most likely an axial flow or propeller type, in which case, the required
BHP is usually highest at shut-off condition. Check that the motor is not being