Head, in short, is the height at which a pump can raise water up to.

In terms of fundamental units, it is a measure of energy per unit weight of water, expressed as an equivalent height of water.s

$\text{Head}=\frac{\text{Energy}}{\text{Weight}}$, this means that we express head in feet of water because $\frac{\text{lb}\cdot\text{ft}}{\text{lb}}=$feet.

But first, let’s define some fundamentals.

For flowing water, the mechanical energy consists of pressure energy, kinetic energy, and potential/elevation energy:

\text{Energy}=\text{Pressure Energy}+\text{KE}+\text{PE}

\text{Energy}=PV+\frac{1}{2}mv^2+mgh

Divide Energy by Weight,

\frac{\text{Energy}}{\text{Weight}}=\frac{PV}{\text{Weight}}+\frac{\frac{1}{2}mv^2}{\text{Weight}}+\frac{mgh}{\text{Weight}}

Weight, or $W=mg$

$\frac{E}{mg}=\frac{PV}{mg}+\frac{½mv^2}{mg}+\frac{mgh}{mg}$ is how we could write our equation, now let’s start simplying.

\frac{E}{mg}=\frac{PV}{mg}+\frac{\frac{1}{2}v^2}{g}+h

So pressure head, $h_P$ is $\frac{PV}{mg}$, or since we know volume equals mass divided by density $V=m/\rho$, we can substitute that into the equation to get $\frac{P(m/\rho )}{mg}$ or $\frac{P}{\rho g}$. The velocity head, $h_v$ is $\frac{½v^2}{g}$ and the elevation head, $h_e$ equals $h$ (or denoted by $z$ in some texts).

Remember to make a point about using consistent units!

• P = lb/in² or lb/ft²
• m = slinch or slug
• V = in³ or ft³
• v = in/s or fps