Lessons · Engineering · pressure at depth
Pressure at depth: the weight of the column above you
In a fluid at rest, pressure rises with depth as p = ρ g h. Only depth, density and g matter; the shape of the container does not.
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
A tank's bottom drain valve is rated at 100 kPa and the tank is 12 m tall. Whether that valve holds is one multiplication, and a valve that lets go at the bottom of a full tank empties it onto whoever is standing there.
How to think about it
Density times g times depth gives gauge pressure, the amount above atmospheric. Add about 101.3 kPa if the question wants absolute. Ignore the tank's width; a standpipe and a lake at the same depth push the same.
Worked example
p = ρ g hPressure is the weight of the column of fluid above the point, per unit area.
Water ρ = 1000 kg/m³, g = 9.81 m/s², depth 5 mThe three inputs.
p = 1000 × 9.81 × 5 = 49,050 Pa = 49.05 kPa gaugeNearly half an atmosphere, five metres down.
Absolute: 49.05 + 101.3 = 150.35 kPaAdd the atmosphere pressing on the surface, if the question wants absolute.
Your turn
Depth 2 m of water. Write the gauge pressure.
p = 1000 × 9.81 × = 19,620 Pa
Solve one, graded on the server
The trap
Thinking the shape of the tank matters. A narrow standpipe 5 m tall pushes on the bottom valve exactly as hard as a lake 5 m deep. The width of the tank changes the total force on the floor, never the pressure.