Question

Find the hydrostatic force on the pictured region.

Answer 1

Notes Practice Assignment

Hide Mobile Notice   

MOBILE NOTICE

You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.

Section 2-4 : Hydrostatic Pressure And Force

In this section we are going to submerge a vertical plate in water and we want to know the force that is exerted on the plate due to the pressure of the water. This force is often called the hydrostatic force.
There are two basic formulas that we’ll be using here. First, if we are dd meters below the surface then the hydrostatic pressure is given by,
P=ρgdP=ρgd
where, ρρ is the density of the fluid and gg is the gravitational acceleration. We are going to assume that the fluid in question is water and since we are going to be using the metric system these quantities become,
ρ=1000 kg/m3g=9.81 m/s2ρ=1000 kg/m3g=9.81 m/s2
The second formula that we need is the following. Assume that a constant pressure PPis acting on a surface with area AA. Then the hydrostatic force that acts on the area is,
F=PAF=PA
Note that we won’t be able to find the hydrostatic force on a vertical plate using this formula since the pressure will vary with depth and hence will not be constant as required by this formula. We will however need this for our work.
The best way to see how these problems work is to do an example or two.