You will also find another kind of pressure unit, which appears to be a length. These units include inches of water, inches of mercury (Hg), or the height of some other liquid of known density. These units, while measured in length units, still represent a pressure. The length describes the pressure exerted by a column of liquid of the given height, and is known as the head.
For example, a pressure reading of 1 inch of water (1 in. H₂O) means that the exerted pressure is equal to the pressure exerted by a column of water 1 inch high, or that a column of water in a U-tube would be displaced 1 inch by the pressure being measured. Similarly, a reading of 12 inches of mercury (12 in. Hg) means that the measured pressure is sufficient to support a column of mercury 12 inches high.
What is really being expressed, even though it is not mentioned in the pressure unit, is the fact that a certain quantity of material (water, mercury, etc.) of known density will exert a certain definite force upon a specified area. Pressure is still force per unit area even if the pressure unit refers to the height of some liquid.
This means that a \(\ft{1}\times\ft{1}\times\ft{1}\) cube of water weighs \(\lb{62.4}\text{.}\) To find the pressure of a column of water 1 foot high, divide the weight of the water by the by the area of the of the base of the cube.
\begin{equation*}
\textrm{1 foot of head} = \frac{\lb{62.4}}{\inch{144}^2} = \psi{0.433}
\end{equation*}
Figure2.7.6.One cubic foot of fresh water weighs 62.4 pounds.
This equation indicates that a 1 foot head of fresh water exerts a \(\psi{ 0.433}\) pressure at the base.
Each additional foot of head will increase the pressure by an additional \(\psi{0.433}\text{,}\) so a head \(h\) (of water, in feet) is equivalent to a pressure
\begin{equation*}
p = \left[\frac{\psi{0.433}}{\ft{1}}\right] h
\end{equation*}
For liquids other than fresh water, the calculation must be adjusted for density. Recall that the specific gravity of a substance is defined as the ratio of the density (or specific weight) of a substance to the same value for water
Fresh water has a specific gravity of 1; salt water has a specific gravity of 1.031, so it is slightly denser than fresh water; and mercury has a specific gravity of 13.633, so it is much denser than water.
To find the pressure in psi of a head \(h\) of a fluid with a specific gravity s.g.
\begin{equation}
p = \left[\frac{\psi{0.433}}{\ft{1}}\right ] (\textrm{s.g.})\ h\tag{2.7.1}
\end{equation}
Example2.7.7.Pressure to Head.
What head of water will cause a pressure of \(\psi{1}\text{?}\)
Answer.
\begin{equation*}
h = \ft{2.31}
\end{equation*}
Solution.
Since \(\ft{1}\) of water is equivalent to \(\psi{0.433}\text{,}\) we can create a unit-factor to solve for how many feet are equivalent to \(\psi{1}\text{.}\)
\begin{equation*}
h = \psi{1} \times \left[\frac{\ft{1}}{\psi{0.433}}\right] = \ft{2.31}\text{.}
\end{equation*}
Example2.7.8.Head to pressure.
What is the pressure in pascals caused by a \(\m{2}\) head of fresh water?
