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Chapter 18
Water pressure
The water pressure at any depth is due to the weight of water above the point in question and increases uniformly with depth below the surface. From this it can be seen that the pressure at any depth will vary with the depth below the surface and the density of the water.
Pressure at any depth
Consider an area of 1 sq m at the water level as shown by ABCD in Figure 18.1. The water pressure on this area is zero as there is no water above it. Now consider the area EFGH which is submerged to a depth of 1m below the surface. There is 1 cu. m of water above it. Let the density of the water be `w' tonnes per cu. m. Then the pressure on this area is `w' tonnes per sq m, and the total pressure or thrust on an area of `A' sq m whose
centre of gravity is 1 m below the surface, will be wA tonnes.
Next consider the area IJKL whose centre of gravity is 2 m below the surface. The pressure is now due to 2 cu. m of water and will be 2 w tonnes per sq m. Also, the total pressure or thrust on any area whose centre of
gravity is 2 m below the surface, is 2 wA tonnes.
Similarly, the pressure on the area MNOP will be 3w tonnes per sq
metre, and the total pressure or thrust on any area whose centre of gravity is 3 m below the surface will be 3 wA tonnes.
The following formulae may now be deduced:
Total pressure or thrust w A h tonnes
where
h the depth of the centre of gravity below the surface
w the density of the water in tonnes/m3, and A the area in sq m.