\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \ten#1{\times 10^{#1}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\)

Pressure

To find the pressure at a point A in a fluid, we first need to find a refeernce point in the same connected fluid where the pressure $P_0$ is already known:

• If the pressure is given to us at some point, then that is the reference point.
• A surface of the fluid can be the reference point if it is in equilibrium with...
• the open atmosphere, in which case $P_0=P_{atm}=$101,000Pa (unless otherwise specified)
• a vacuum, in which case $P_0=0$
• a gas with a known pressure $P_0$

Once we've found the reference point, the pressure at point A is $$P=P_0+\rho_{f}gd$$

Some tips:

• If point A is below the reference point, then $d$ is positive; if above, then $d$ is negative.
• All points at the same level in a fluid have the same pressure.
• Use the density of the fluid. For water, use $\rho_f=1000{\rm kg/m^3}$.
• The reference point must be in the same connected fluid as point A; every fluid has its own reference point.
• For relatively small scales, a single continuous gas can be assumed to have the same pressure everywhere.