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
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
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)
Therefore water pressure depends only on depth.