Head

From Chemepedia

In pumping systems, the "head" form of the mechanical energy balance is generally used. Head is useful because it evaluates a pump’s ability to do a job. Most pump applications involve moving fluid from a lower level to a higher level. For instance, if you have to move liquid up 100 feet and your pump doesn’t have at least 100 feet of head, then there is no chance it will work. The pump will need at least 100 feet plus the friction loss to get the required flow at the discharge point.

Another advantage about head is it is independent of the type of fluid being pumped (assuming the viscosity is relatively low and similar to water). Whether you are pumping water or a heavy caustic solution, the head achieved will be the same. The pressure at the discharge of the pump, however, will be higher for the heavier solution.

The steady-state mechanical energy balance for an incompressible fluid between any two points (1 and 2) in a system with one inlet and one outlet can be arranged as

            (1)

Where each quantity in the above equation has dimensions of height. Defining each of the terms as a head, we can write

            (2)

where is the sum of the pressure (or static head) head, velocity (or dynamic) head, and elevation at the same point. In other words

            (3)

So, for instance, if we want to pump a fluid from a height of to a height of between two large open air tanks, (2) becomes

            (4)

which can be rearranged as

            (5)

Which hopefully reinforces why the the concept of head is used. Here, the head that is transferred by the pump to the fluid must equal the height difference between the fluid in the two tanks plus the viscous head generated due to frictional losses.

Viscous head loss

The head loss due to viscous flow can be broken into two contributions

            (6)

where is the head loss due to fluid flow in pipes of constant diameter and is the head loss due to changes in fluid flow through fittings, pipe bends, contractions, expansions, etc. In general

            (7)

where

  • is the Darcy friction factor associated with section of a piping system with a constant diameter
  • is the loss coefficient associated each fitting, pipe bend, contraction, or expansion.

For instance, as shown in the images below, the system will have 3 major loss terms and 5 minor loss terms.

Figure 1. Major losses representation
Figure 2. Minor losses representation