# Pressure of Liquid at Depth (M)

Q:
how do you calculate the pressure of a liquid at depth (M) knowing the liquids density?
- Phillip Giles
Park House School, Newbury
A:
The pressure at the bottom of the liquid is calculated as P1 + rgM, where P1 is the pressure above the liquid (in Pascals), r is the density of the liquid (in kilograms/meter^3), g is the earth’s gravitational acceleration constant (9.80 meters/second^2), and M is the vertical depth of the liquid (in meters). The units of the calculated pressure would be Pascals.

For example, the pressure beneath 10 meters under the surface of a lake with atmospheric pressure of 1.01 x 10^5 Pascals would be calculated as follows:

1.01 x 10^5 Pa would be P1, as it is the pressure above the liquid
9.80 m/s^2 would be g
1.00 x 10^3 kg/m^3 would be r, as it is the density of fresh water
10 m would be M, as it is the depth of the water

So the calculation would be Pressure = 1.01 x 10^5 + (1.00 x 10^3)*(9.80)*(10) = 199000 Pascals of pressure

Hope this helps

(published on 10/22/2007)

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