Pressure and hydrostatics
In a still liquid, pressure increases with depth because each layer carries the weight of the liquid above. It acts equally in all directions at a point and always pushes normal to any surface it touches.
This simple fact designs a great deal of civil infrastructure. Water tanks, dam faces, sluice gates, retaining walls holding back water, and pipes all feel a pressure that grows linearly from zero at the free surface. The total force on a vertical wall is the area of that triangular pressure diagram, and it acts at one third of the height from the base.
Pressure is often expressed as a head: the height of a column of liquid that would produce it. Ten metres of water is roughly one bar, about 98 kPa. Piezometers and manometers measure pressure by the height of a liquid column.
On a submerged plane surface, the resultant force equals the pressure at the centroid times the area, and it acts at the centre of pressure, which lies below the centroid.
p = ρ g hForce on a vertical wall of height H, per metre width: F = ρ g H² / 2, acting H/3 above the basePlane surface: F = ρ g h̄ A; centre of pressure depth = h̄ + I_G / (A h̄)
Problem. A tank wall holds 4 m of water. Find the force per metre and its line of action.
- F = 1000 × 9.81 × 4² / 2 = 78 480 N/m.
- It acts 4/3 = 1.33 m above the base.
Answer. 78.5 kN per metre, 1.33 m above the base
Quick quiz
1How does pressure vary with depth in still water?
Linearly.
2Where does the resultant on a vertical wall act?
At one third of the height from the base.
3Approximately what pressure is 10 m of water?
About 98 kPa (about 1 bar).
References and further reading
Standard texts, listed in no order of merit. We do not copy text, figures, tables or solved problems from any book; our explanations and examples are original.
- P. N. Modi, S. M. Seth, Hydraulics and Fluid Mechanics including Hydraulic Machines, Standard Book House, latest edition.
- V. T. Chow, Open-Channel Hydraulics, McGraw Hill, 1959.
- K. Subramanya, Flow in Open Channels, McGraw Hill Education (India), latest edition.
Free and official sources
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