Consider the hydrostatic equilibrium (v = 0). The equation is reduced to:
0 = -∇p + Ïf
Let the air pressure be p0. Solve the hydrostatic pressure p(h) at a depth h in the pool (water density Ï = constant) when the external force is f = -gk, where g is the acceleration of gravity and k is the unit vector in the upward direction. (Note: you can select z = -h.)