|Variation of Pressure in a Fluid at Rest|
When a fluid is at rest, then all points at the same depth must be at same pressure. That is the pressure at the same dept of a fluid at rest must be same. However, it varies with depth since it will have weight of the fluid on the top of it.
Po is the atmospheric pressure = 1.00 atm = 1.013 × 10^5 Pa
g is the acceleration due to gravity
ρ is the density of the fluid
h is the depth of the point at which the pressure P is to be calculated
A is the cross sectional area
Consider the above figure. Since the fluid is at rest the net force is zero:
PA – mg – PoA = 0
However Mass (M) = Density (ρ) × Volume (V) = Density × Area × Height = ρAh. Thus, we can write:
PA – PoA – ρAhg = 0
On simplifying we get:
P = Po + ρgh
Hence, the pressure P at a depth h below the surface of a fluid open to the atmosphere is greater than the atmospheric pressure by an amount ρgh. The difference in pressure between two points of unequal depth causes buoyant force.