Problem 4.9.5

A centrifugal pump delivers water from an open tank at 180 degrees Fahrenheit at a rate of 100 gallons per minute. The outlet from the tank is 10 feet above the pump center-line. Pump inlet line is 15 feet in length and has three 90 degrees elbows. Pipe is 2 inch schedule 40. What is the net positive suction head available to the pump?

Solution:

At 180 degrees Fahrenheit, vapor pressure of water can be read from steam tables or other source as 7.51 psi. Viscosity of water is 0.35 cP. Density of water = 60.6 pounds per cubic foot. Inside diameter = 2.067 inches.

Volumetric flow rate is 100 gallons per minute or 0.223 cubic foot per second.

Cross sectional area is 0.023 square foot.

Velocity of the water is 9.561 feet per second.

Reynolds number is 4.243 time 10⁵. For the relative roughness of 8.72 times 10^-4, friction factor is 0.00494.

For three 90-degree elbows, equivalent length is 30 feet.

Discharge line from the tank contributes towards pressure loss. This loss can be represented as contraction loss and is equal to 5 feet of pipe length.

Total equivalent pipe length is 15 plus 30 plus 5 or 50 feet.

Frictional losses are found to be 8.144 foot pound-force per pound-mass.

Applying Bernoulli equation between tank surface and pump inlet, P₁ over rho plus Z is equal to P₂ plus rho plus h_f

P₂ is calculated as 2229 foot pound-force per pound-mass.

Net positive suction head is P₂ over rho minus P⁰ over rho. NPSH is found to be 18.93 foot pound-force per pound-mass.