Chemical & Process Technology

Cheat Sheets: 2.31 or .433?
The Numbers May Be Different, But the Result Is the Same

No, it’s not a new song by the band Chicago. (Remember “25 or 6 2 4”?) These numbers are the conversion factors that relate pump head with pressure. As established in my previous column (“Pump Secrets Lost in Time,” Jan. ’08), head is a measure of energy. The units of energy are expressed in feet or meters. Pressure is a force applied to a unit of area, such as a pound of force applied to a square inch of area, or PSI. For water, we can say that had in feet divided by 2.31 is pressure in PSI, and pressure in PSI multiplied by 2.31 is head in feet. Stated mathematically:

Head (ft.)/2.31 = PSI and PSI x 2.31 = Head (feet)

It is equally correct to convert head into pressure and vice versa with the factor .433. Head in feet multiplied by .433 is pressure in PSI, and pressure divided by .433 is head in feet. Mathematically:

Head (feet) x .433 = PSI and PSI/.433 = Head (feet)

Math-challenged people may find it easier to divide by 2.31, rather than multiplying by a decimal, but the result is the same.

Where does the conversion number 2.31 come from? A cubic foot of ambient water weighs 62.4 pounds. A square foot of area contains 144 in2. If we divide one by the other, we get our conversion number 2.31 (i.e., 144/62.4 = 2.31) (Figure 1). Remember, some people prefer .433, the other conversion: 62.4/144 = .433. Here is another way to understand the same concept. If I poured one pound of ambient water into a long, narrow receptacle that measures one in2, the water would fill that receptacle to a height of 2.31 feet (See above figure).

Here is a practical example. The waterfall is at the eastern escarpment in South Africa. Some Tarzan movies were filmed here. Tarzan would jump off the waterfall to the river below and wrestle a rubber crocodile, while Cheeta the chimp danced and did back flips on the shore.

These falls drop 213 feet to the river below. What is the pressure of the falling water column as it strikes the surface of the river below?

213 feet/2.31 = 92 PSI or 213 feet x .433 = 92 PSI.

The falling water column strikes the river down below at 92 PSI. (You’d have to make a small correction for the acceleration and the wind resistance, so it isn’t precisely 92 PSI.)

With pumps, a standard water pump developing 70 feet of head would exhibit 30 PSI of differential pressure across the pump (i.e., 70 feet/2.31 = 30 PSI.

The term “head” is the constant for the pump manufacturer. A pump that develops or generates 70 feet of head can elevate any liquid 70 feet. If you think of the pump’s performance in head, it doesn’t matter what the liquid is. It could be any liquid from liquid propane to liquid mercury.

For ambient water, divide feet of head by 2.31 (or multiply by .433). If the liquid is not water, then you must factor the specific gravity of the liquid.

Specific gravity is the relative density of a liquid compared to water. We say that ambient water (at sea level) has a specific gravity of 1.0. Another liquid might be denser (heavier) or less dense than water. For example, sulfuric acid is twice as dense as ambient water; it has a specific gravity of 2.0.

Returning to the pump that develops 70 feet of head — if pumping sulfuric acid, the pump will exhibit 60 PSI across the pump (i.e., 70 feet/2.31 x sp. gr.(2) = 60 PSI).

Gasoline has a specific gravity of 0.75. This means an equal volume of gasoline would weigh ¾ or 75 percent the weight of water.

Returning to that same pump that develops 70 feet of head — if gasoline is the liquid, the differential pressure across the pump will be 23 PSI (i.e., 70 feet/2.31 x sp. gr. (0.75) = 23 PSI.

It’s easier in the metric system.

Meters of head x 10 = kilopascals of pressure.

The maintenance engineer or mechanic must understand head to converse with the pump manufacturer. The maintenance engineer must also know how to relate head (on the pump curve) to the pressure in the pipes.

Rip these pages, copy them and share them, or store this edition of Flow Control in a safe place for future reference. This is your CHEAT SHEET of useful pump information.