How do I derive the formula for lithostatic (overburden) pressure?

Question

The title pretty much says it. I have the formula: $P = \\rho g h$ where $\\rho$ is the density, $h$ is how deep the pressure is in the Earth and $g$ is the gravitational acceleration(?).I don't get the units either. If I substitute the units for each term I get this: $$P = \\frac{\\mathrm{kg}}{\\mathrm{m}^3} \ imes \\frac{\\mathrm{m}}{\\mathrm{s}^2} \ imes \\mathrm{m} = \\frac{\\mathrm{kg}}{\\mathrm{m}*\\mathrm{s}^2}$$ Shouldn't it be something like $P = \\dfrac{\\mathrm{kg}}{\\mathrm{m}^2}$? As far as I'm concerned that's the unit for pressure. Where do I get this formula from and how do I derive the unit of measurement?

Answer 1

You are actually on exactly the right track! Recall that pressure is Force/Area, commonly given as N/m^2. Since a Newton is kg*m/s^2, then Pressure = N/m^2 becomes Pressure = kg/(m*s^2), exactly as you derived.