10. Force Due to Liquid Pressure by Integration
by M. Bourne
The force F on an area A at a depth y in a liquid of density w is given by
`F = wyA`
The force will increase if the density increases, or if the depth increases or if the area increases.
So if we have an unevenly shaped plate submerged vertically in a liquid, the force on it will increase with depth. Also, if the shape of the plate changes as we go deeper, we have to allow for this.
So we have:
Now, the total force on the plate is given by
x is the length (in m) of the element of area (expressed in terms of y)
y is the depth (in m) of the element of area
w is the density of the liquid (in N m-3)
(for water, this is w = 9800 N m-3)
a is the depth at the top of the area in question (in m)
b is the depth at the bottom of the area in question (in m)
Find the force on one side of a cubical container `6.0` cm on an edge if the container is filled with mercury. The weight density of mercury is `133` kN/m3.
A right triangular plate of base `2.0` m and height `1.0` m is submerged vertically in water, with the top vertex `3.0` m below the surface.
Find the force on one side of the plate.