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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.