Page Description Equation
The absolute pressure $P$ of a fluid of density $\rho$ at a depth $h$ from its surface that is exposed to an atmospheric pressure $P_0.$ This equation says that the absolute pressure applied to the surface at depth $h$ is the sum of the pressure applied at the surface (depth 0) plus the pressure applied by the weight of the volume above depth $h.$ It is also the magnitude of the reaction force (per unit area, i.e. pressure) acting upward on the volume of water above the depth $h$ by Newton’s third law. \[ P=P_0+\rho gh \]
gauge pressure. This is the pressure of the column of water with depth $h$ resulting from the water’s weight alone (not including pressure on the water from surrounding water or air media). \[ P_{\mathrm{gauge}}=P-P_0=\rho gh \]
weight of a rectangular cylinder of density $\rho,$ mass $m,$ cross sectional area $A,$ and height $h.$ \[ F_{\mathrm{gauge}}=P_{\mathrm{gauge}}A=\rho ghA=\rho gV=mg \]
weight-density (weight per unit volume) \[ \rho g=mg/V \]
weight in terms of density \[ \rho gV=mg \]
open-tube manometer
mercury barometer \[ \begin{align*} 0 &=P=P_0-\rho gh\\ P_0 &=\rho gh \end{align*} \]
mercury barometer, cf. p. 16 \[ P=P_0+\Delta P_0 \]
units, pressure \[ \left[\rho gh\right] =\frac{\mathrm{M} }{\mathrm{L}^3}\frac{\mathrm{L} }{\mathrm{T}^2}\mathrm{L} =\frac{1}{\mathrm{L}^2}\frac{\mathrm{ML}}{\mathrm{T}^2} =\frac{\mathrm{F}}{\mathrm{L}^2} \]
atmospheric pressure \[ P_0=1\cdot\mathrm{atm}=1.013\times{10}^5\cdot\mathrm{Pa} \]
equation of continuity \[ A_1v_1=A_2v_2=\mathrm{constant} \]
Archimedes’ Principle \[ F_b=F_{g,\mathrm{fluid}} \]
Bernoulli’s Equation \[ P+\frac{1}{2}\rho v^2+pgy=\mathrm{constant} \]