Pressure and upthrust

Pressure 

What is pressure?

Pressure due to a liquid

Pressure due to a liquid

We have seen in this post about the concept of pressure that a solid exerts on a surface.

Today we are going to look at the pressure that a liquid exerts on the bottom of a container in which it is present.

Fig 1 below shows a container containing an unknown orange liquid. The depth of liquid in the container is h. The density of the liquid is denoted by the letter ρ.

Fig 1

Fig 2 below represent the same container but this time in 3 dimensions. The container is in the form of a cuboid. The liquid will thus be in the form of a cuboid with cross-sectional area and height h.

Fig 2

Now how do you obtain the pressure that the liquid is exerting on the bottom of the container?

The equation for pressure is

Pressure = Force Applied /Surface area

              = Force applied by liquid/surface area over which pressure is applied

              = Weight of liquid /Cross-sectional area A

              = mg /A

               = (Volume of liquid *density*g)/A

                = (Ah *ρ)*g/A

                 = h*ρ*g

                 = hρg

Where g is the acceleration due to gravity.

Example

A bottle of water of density 1000 kg/m³ has water of depth 0.10 m in it. If the acceleration due to gravity,g, is 9.81 m/s² , calculate the pressure due to the water on the bottom of the container.

Pressure due to water =hρg

= 0.10*9.81*1000

=981 Pascal (Pa)

What is pressure ?

When you have a force that is applied on a surface over a given surface area then you say that a pressure is being exerted on the surface.

Fig 1

Fig 1 shows a small wooden block placed on a wooden sheet. As you know every object has a weight. This weight as you would remember is a force of attraction that the earth is exerting on the object. Thus it is a downward force.

Hence we can deduce that block of wood due to its weight is applying a force F on the sheet. The force F  would act as shown in fig 2 below.

Fig 2

But we also know that the weight of the object, the force applied on the wooden sheet, is being applied over a surface area A. That surface area is shaded black in fig 3 below.

Fig 3

The pressure exerted on the wooden sheet by the wooden blockis thus the force acting perpendicularly per unit surface area.

Hence to calculate the pressure we have to use the equation below:

Pressure exerted = Force applied / surface area

The unit of pressure is thus the N m^-2

The pressure is a scalar quantity since it is obtained by dividing a vector quantity by a vector quantity.

Pressure and upthrust

Pressure 

What is pressure?