PUMP SYSTEM FORMULAS (IMPERIAL UNITS)

Many of these applets have been replaced with more conventional web apps

(problem viewing applets)

Flow vs. velocity

Normally, the flow rate is given, it is fixed by the user or the requirements of the process. For a new system the pipe diameter is unknown, with the flow rate and a trial estimate of the pipe size it is possible to see if the velocity will be in the desirable range as given at this page.

Pressure vs. pressure head or fluid column height

Head is one of the main characterisitics of a pump. In the imperial system it is measured in feet. If the maximum discharge head of a pump is say 30 feet, the fluid will be able to get to 30 feet of height above the discharge and the flow will be zero. The head of the pump depends on the flow rate and it is zero at the maximum head and diminishes as the flow increases. To verify the discharge head of a pump, a pressure gauge is used. Pressure gauges measure in units called psi or pounds per square inch. The formula gives the conversion of pressure to head.

and to do your own head and pressure calculations with this java applet

see Figure A-1 at bottom for location and meaning of subscripts (more info)

Pump shaft brake power

Power is given by the combination of four items: the specific gravity SG, the total head , the flow rate Q and the efficiency of the pump eta . The specific gravity SG is the ratio of the fluid's density to that of water at standard conditions, for water the value of SG equals 1. The total head is normally calculated for the flow rate of the system and depends on static head, pipe friction loss and equipment loss, it can also be measured with pressure gauges. Two pressure gauges are required, one on the discharge and one on the suction side of the pump. The difference between these two measurements is taken and the 2nd formula above is used to convert to head. And finally, the efficiency of the pump must be known, this is usually obtained from the pump manufacturer's total heads vs. flow curve of the pump (see typical pump curve). The units are as specified in the formula, US gallons per minute are used as opposed to imperial gallons per minute.

Power at the pump shaft through the motor

Since more often than not, a pump is driven by an electric motor, it is possible to determine the power consumed by a pump by looking at the power consumed by the motor. The volts V are the volt level that is supplied to the motor. In industrial applications, this is often 3 phase, 575 volts. For residential and commercial installations, we encounter single phase, 110 or 220 volts. If the voltage is single phase then we ignore the square root of 3 in the formula. The amps A is a unit of measuremnt of current and this is normally measured with an ammeter. The efficiency of the motor eta is given by the manufacturer and for a recent motor varies between 0.92 and 0.96. P.F. is the power factor of the motor and is proprotional to the phase difference between the current and the voltage. P.F. has similar values to those of efficiency. Typical values of efficiency and power factor for industrial motors can be found here.

Specific gravity vs. fluid density

For typical values see the pump glossary.

This is the definition of specific gravity SG. The density of water is taken at standard conditions such as 60 F and 14.7 psia pressure. The density of water at standard conditions is 62.34 lbm/ft3.

Kinematic viscosity

Nu vs. dynamic (absolute) viscosity mu

This is the relationship between kinematic viscosity nu n and dynamic viscosity mu m. These are often used interchangeably, and this is correct when the fluid SG is one however incorrect when it is not.

Kinematic viscosity vs. dynamic (absolute) viscosity

This is the relationship between viscosity expressed in Saybolt Universal Second SSU and the viscosity in centiPoise.

Kinematic viscosity

SSU vs. cSt

Reynolds number

and to do your own Reynolds number calculations with this java applet

Pipe friction loss

see Appendix B in tutorial.pdf

and do your own calculations with this java applet

Fittings friction loss

see Appendix C in tutorial.pdf

do your own calculations with this java applet

Friction factor

for the laminar flow regime Friction factor for the turbulent flow regime

Friction factor for the turbulent flow regime

Swamee-Jain equation

N.P.S.H.A. (Net positive suction head available)

see Figure A-2 at bottom and do your own calculations with this java applet and view this help file to learn more about NPSHA

Specific speed

and also specific_speed_primer.pdf

and do your own calculations with this java applet

Suction specific speed

and also specific_speed_primer.pdf

and do your own calculations with this java applet

Affinity laws

Flow vs. impeller speed and diameter

and do your own calculations with this java applet

Affinity law

Head vs. impeller speed and diameter

and do your own calculations with this java applet

Affinity law

Power vs. impeller speed and diameter

and do your own calculations with this java applet

Figure A-1

Figure A-2

Symbols

A: area: in2 (inch square)
D: pipe diameter: in (inch)
f: pipe friction factor
g: acceleration due to gravity: 32.17 ft/s2: ft/s2 (feet/second squared)
L: length of pipe: ft
p: pressure: psi (pound per square inch)
P.F.: power factor

P: power: hp (horsepower)

Re: Reynolds number
SG: specific gravity; ratio of the fluid density to the density of water at standard conditions
q: volumetric flow rate: ft3/s
V: volume: ft3
v: velocity: ft/s
z: vertical position: ft

Greek terms
D: delta: the difference between two terms
e: epsilon: pipe roughness: ft
n: nnu: kinematic viscosity SSU (Saybolt Universal Second)
h: efficiency
m: mu: dynamic viscosity
r: rho: density: lbm/ft3
g: gamma: specific weight: lbf/ft3