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)

Volume and volume of regular objects

The volume of an object is the space that the object occupies.

It is a scalar quantity and its SI unit is the cubic metre (m³)

The unit for the volume of object can also be derived from any other unit for length such as the cubic centimetre, cubic kilometre, etc

We are now going to see how the volume of an object is determined.  The method to determine the volume of the object depends on the nature of the object as shown below.

Volume of regular objects

Regular objects are those that have a plane of symmetry. It simply mean that if the object is cut along the plane of symmetry then the two parts will be similar to each other with the same volume.

The volume of regular objects is determined by measuring the dimensions of the object and finally using using an equation. The following are different regular objects and the equations used.

Cuboid

  

Cube

Volume = length * length * length

            = L³

Since all the sides of the cuboid are of equal length.   

Sphere

since r = d/2 then

As you can see all regular objects are determined by measuring the dimensions and then using equations to determine the volume. I would try with time to add as much of regular objects and their equations. If you require the equation for any regular shape then leave message in the comments below.

Gravitational potential energy

It is simply the energy that a body possesses due to its position above the surface of the earth. There is a second form of potential energy called elastic potential energy that we are going to see later.

The equation to calculate the gravitational energy is

Gravitational potential energy Ep = mgh

Where m is the mass of the object
g is the acceleration due to gravity
h is the height of the object above the ground


Let us have a look at example where the gravitational potential energy of an object.

Example 1

A high jumper has a mass of 62 kg. He jumps to a maximum height of 2.3 m. If the acceleration due to gravity is 9.81 ms^-2, calculate the gravitational potential energy of the object.

Gravitational potential energy Ep = mgh
= 62*9.81*2.3
= 1398 kg
= 1400 kg


You should also know how to obtain the mass or the height of an object if the gravitational potential energy is known.

Let us see an example.

Example 2

A person has a potential energy of 11000 J. If the mass of the person is 85 kg and the acceleration due to gravity is 9.81ms^-2, determine his height above the ground.

Gravitational potential energy Ep = mgh
11000 = 85*9.81*h
h = 11000/ (85*9.81)
` = 13.2 m
= 13 m

I hope you have understood. If you have any questions, leave them in the comment section below. See you later my students.

If you want to test your knowledge of gravitational potential energy, do the following questions leave the answer in the comment section?

Question

A bird of mass 0.12 kg is flying at a height of 12 m above the ground. If the acceleration due to gravity is 9.81 m s^-2, what would be the gravitational potential energy of the bird?

If the bird has a gravitational potential energy of 110 J, at what height would it be flying?