The pressure underwater depends on depth, but why ?

To find out why, a specific example is needed. A swimming pool of 5 meters deep will be used.


1 meter below the surface, the fluid's pressure generates a downward force whose magnitude is . Similarly, below 2 meters, the pressure generates an upward force of magnitude . The pressure is greater than the pressure , because more weight of the water is supported 2 meters under. The extra weight is mg, where m is the mass of the fluid and g is the magnitude of the acceleration due to gravity.

Setting the sum of the vertical forces equal to zero, it is found that

or

The mass is related to the density p and the volume V of the water between 1 meter and 2 meter by m=pV.

Since, V=Ah (Voulume = Area x height)

becomes



which is




Therefore water pressure depends only on depth.