13. (Problem Solving)

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 $P_{0} = P_{a t m} =$ 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 $P = P_{0} + ρ_{f} g d$

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 $ρ_{f} = 1000 k g / m^{3}$ .
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.