There is often considerable confusion among students when it comes to the definition and use of pumping head. This is understandable since head is a concept that was developed many years ago as a short-cut concept for field engineers when American engineering units (then called the English system) was the only set of units presented to students. American engineering units are still the dominant units used in the U.S. chemical engineering field, but for the most part, the science education of engineers in the U.S. has moved over to the metric system. The concept of head can be a stumbling block in a student's efforts to navigate the waters between these two systems.

The concept of head is related to the mechanical energy balance[Felder & Rousseau]:

Let us begin by examining the units of terms in equation 1 using the American engineering system ([=] means, has units of).

If we convert terms above using the lb_f definition, we obtain three terms with common units of ft lb_f/lb_m. These are not units of head and it is not permissible to ``cancel '' lb_f with lb_m.

What, then, is head? Head is mechanical energy per unit weight. What is weight? Weight is the force due to a mass in a gravity field, and it has units of force which are newtons (N) in the metric or SI system, or lb_f in the American engineering system.
 

 

The distinction between weight and mass is often forgotten since we all live in the Earth's gravitational field. We say, ``That box weighs 90 kilograms," even though kilograms are units of mass rather than weight. The correct unit of weight in the metric system, the newton, is not used in common language (Even in countries where they use the metric system they do not use the newton; they say ``I weigh 50 kilos.").

In the American engineering system the situation is at once simpler and more complicated. In this system the units of both mass and weight are the pound. The lb_f, in fact, is defined with the Earth's gravity field in mind since 1 lb_m weighs 1 lb_f on Earth. It becomes tempting, however, to confuse the two types of pounds with each other and to cancel them in equations, and this can lead to errors.

If we examine equation 1 above, we see that it is written in terms of mechanical energy per unit mass. To rewrite it in terms of mechanical energy per unit weight, or head, we must divide by the acceleration due to gravity, g

We thus see that head, mechanical energy per unit weight, has units of ft which is a particularly easy unit to remember.

Is that the whole point? Why bother with all of this mess just to use a simple unit? Engineers deal with many types of units all the time and could certainly learn to deal with other units such as ft lb_f/lb_m, or N, or whatever.

The desirability of using head in the mechanical energy expression is obscured in the calculations shown above by the fact that no numbers have been used. Let us examine the head produced by a pressure difference of 50 lb_f/ft² in a system pumping water.

Thinking in terms of head allows an engineer to have some intuition about the amount of mechanical energy per unit weight under consideration. Let us examine elevation head. The value in ft of the elevation head is the height difference between two reference points. Now if we express the velocity term in head units (velocity head ºD (v²)/2 g) we can understand what, for example, 10 ft of velocity head means. It is the equivalent amount of mechanical energy per unit weight to that represented by 10 ft of water. Likewise if the pressure term is expressed in head units (pressure head ºD P/rg), a similar understanding is obtained. In pumping this is particularly useful since we can get a handle on the characteristics of a pump by taking about the developed head of the pump. The developed head of a pump represents the height to which a fluid may be lifted by the pump in a frictionless piping system. If the pump is not used to lift fluid, we still can understand that the pump can use its ability to do work (produce mechanical energy per unit weight) to produce elevation, velocity, or pressure head or any combination of these.

In summary, ft of head is a unit of length. It expresses the mechanical energy per unit weight of a flowing system. It may be converted to other systems by using the conversion factors for length. When you do this you must remember that you are keeping track of a quantity which expresses mechanical energy per unit weight. In the SI system, m of head has exactly that meaning. Note that in the SI system N m/kg (the analogous expression to ft lb_f/lb_m) is not numerically equal to m of head. This is because the conversion factor for kg  m/s² to N is one, rather than being numerically equal to g in the SI unit system (check this to convince yourself).

References

[Felder & Rousseau]

 Felder, Richard M. and Ronald W. Rousseau, Elementary Principles of Chemical Processes, 2nd Edition (John Wiley, & Sons: New York, 1986).

This document was translated from L^AT_EX by H^EV^EA.