Discussion
If the gauge pressure at a point well inside a liquid of density ρ in a tank is p , then the depth of the point from the surface of the liquid is (atmospheric pressure is P)
Answer: D
The depth is \(\dfrac{p}{\rho g}\).
The pressure at depth \(h\) is \(P_{\text{abs}} = P + \rho g h\), where \(P\) is atmospheric pressure. Gauge pressure is the pressure above atmospheric, so
\[ \begin{aligned} p &= P_{\text{abs}} - P = \rho g h \\ h &= \frac{p}{\rho g} \end{aligned} \]
Atmospheric pressure has already been taken out of the gauge reading, so options that add or subtract \(P\), or use \(P\) alone, are wrong, and \(\frac{p^{2}}{\rho g}\) does not have the units of length.
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