Question

At the surface of a lake, the pressure is 1 atmosphere. What is the total pressure at a depth of 850m in water?

Answer 1

Pressure is defined as force per unit area acting on a surface. i.e.

  

Where, F is force

and A is area

the total pressure inside a liquid at a depth 'h' is given by

  

Where, P_atm is atmospheric pressure acting on the surface

P_water is pressure due to weight of water above the plane where the pressure to be calculated (i.e at a depth of h)

P_water can be calculated as :

  

Weight of water = mass of water x g (acceleration due to gravity)

Mass of water = Density of water x volume =

Where, is density of water and V is volume of water.

So, Weight of water =

Now, for the given container, volume can be defined as

Volume = Area of the cross section of container x height of the container = A x h

So, Weight of water having a depth h =

.So,

Hence, total pressure at a depth does not depends on the surface area of the container.

So, total pressure at a depth h is given by,

  

In the given question, h = 850 m and density of water = 1000 kg/m³ .

And P_atm = 1 atm =1 x 101325 Pa = 101325 Pa (Pascal) .

The value of g = 9.8 m/s² .

So, total pressure at a depth of 850 m in the lake is

or,

or,   

or,   

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