Hydrostatic Pressure and Force - Applications of integrals

In this part we are going to submerge a vertical plate in water and we wish to know the force that is exerted on the plate because of the pressure of the water. This force is frequently known as the hydrostatic force. There are two main formulas that we'll be utilizing here. 1^st, if we are d meters below the surface after that the hydrostatic pressure is illustrated by,

P = ρgd

In which, ρ and g is the density of the fluid and the gravitational acceleration respectively. We are going to presume that the fluid in question is water and as we are going to be by using the metric system these quantities become,

ρ = 1000 kg/m³

g = 9.81 m/s²

The formula number 2^nd that we need is the following. Presume that a constant pressure P is acting on a surface along with area A. After that the hydrostatic force that acts on the area is,

F = PA

Note: we won't be able to find out the hydrostatic force on a vertical plate by using this formula as the pressure will vary with depth and therefore will not be constant as needed by this formula. Though we will need this for our work.