What to predict the pumping head at the design water flow rate from measurement made at the test water flow rate is very important. The below example will show how to compute the pumping head.

Example 19-1: Determine the pumping heat for the assumption which the static lift (D) was 35 feet and vertical distance (h) of the pressure gauge above the basin curb was 5 feet. At this point, the pressure gauge indicated 25 psig. The 24 inch of pipe was used and the inner diameter was 22.624 inch. Let's assume that the test water flow rate was 14,000 GPM.

(Solution)
First, let's determine the equivalent length of piping and fittings between the point of pressure gauge and the center of inlet pipe.

• Vertical Leg, Length of D - h = 35 - 5 = 30.0 ft
• Horizontal Leg from the center of riser pipe and inlet pipe = 5 ft
• 24", 90^o Welding Elbow (r/d = 1), Equivalent Length = 37.7 ft (from table of friction loss in term of length) Then, total equivalent length = 30 + 5 + 37.7 = 72.7 ft (based on 24 inch pipe)

Second, determine the friction loss in piping and fitting between the point of pressure gauge and center of inlet pipe. The head loss for 24 inch pipe per 100 feet and for 14,000 of test water flow rate is 1.30 ft from the friction table of steel pipe. Then, the friction loss in the feet could be obtained from below;

• Friction Loss = Head Loss per 100 ft x Equivalent Pipe Length = 1.30 / 100 x 72.7 = 0.95 ft

Third, determine the static pressure of test water flow at the center of inlet pipe.

• SPt = Test Pressure - (D - h) - Friction Loss = 25 psig x 2.309 - (35 - 5) - 0.95

(Note: 1 psi = 2.309 feet) = 26.78 ft

Fourth, determine the velocity pressure of test water flow at the enter of inlet pipe.

• Water Velocity @ 24 inch pipe = GPM x 0.1336798 / (0.7854 x (Inner Diameter / 12)²) = 14,000 x 0.1336798 / (0.7854 x (22.624 / 12)² = 670.39 ft/min = 11.17 ft/sec
• Velocity Pressure = Velocity2 / 2g = 11.172 / (2 x 32.174) (1g = 32.174 ft/sec²) = 1.94 ft

Fifth, let's compute the test pumping head

Test Pumping Head = SPt + Velocity Pressure + Static Lift = 26.78 + 1.94 + 35 = 63.72 ft

Sixth, determine the corrected total pressure to the design water flow rate.

• Test Pumping Head = Test Static Pressure + Test Velocity Pressure + Static Lift
• Test Total Pressure = Test Static Pressure + Test Velocity Pressure
• Test Pumping Head = Test Total Pressure + Static Lift
• Test Total Pressure = Test Pumping Head - Static Lift
• Corrected Total Pressure = Test Total Pressure x (Design Water Flow Rate / Test Water Flow Rate)² = (Test Pumping Head - Static Lift) x (Design Water Flow Rate / Test Water Flow Rate)² = (63.72 - 35) x (12,500 / 14,000)² = 22.90 ft

Finally, determine the predicted pumping head at the design water flow rate.

• Corrected Pumping Head = Corrected Total Pressure + Static Lift = 22.90 + 35 = 57.90 ft