Math 1B
§ 8.3 Applications to Physics and Engineering
Overview: 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.
The plate has area A m2 and is submerged in a fluid of
density 𝜌 kg/m3 at a depth of d meters.
The volume of the fluid above the plate is V = Ad so its
mass is m = 𝜌𝑉 = 𝜌𝐴𝑑
⇒ 𝐹 = 𝑚𝑔 = 𝜌𝑔𝐴𝑑
The pressure P on the plate is force per unit area:
!
𝑃 = ! = 𝜌𝑔𝑑
Units: N/m3 = 1 Pascal
When using US units, we write
𝑃 = 𝛿𝑑
where 𝛿 is the weight density of water (𝜌 is the mass density)
For water, 𝜌 = 1000 kg/m3
and
𝛿 = 62.5 lb/ft3
If a constant pressure P is acting on a surface with area A, then the hydrostatic force is
𝐹 = 𝑃𝐴
But pressure increases as depth increases and hence will not be constant.
Example: A tank is 8 m long, 4 m wide, 2 m high, and contains kerosene with density 820 kg/m3 to a
depth of 1.5 m. Find
a) the hydrostatic pressure on the bottom of the tank
b) the hydrostatic force on the bottom of the tank
Example: Find the hydrostatic force on the following triangular plate submerged in water as shown.
Example: Find the hydrostatic force on a circular plate of radius 2 ft. that is submerged 6 ft. in the
water.