Pressure of Liquid at Depth (M)
Most recent answer: 10/22/2007
Q:
how do you calculate the pressure of a liquid at depth (M) knowing the liquids density?
- Phillip Giles
Park House School, Newbury
- 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
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)