cylindrical column. Pressure difference depends on the vertical distance h between the points ( and ), mass density of the fluid ρ and acceleration due to gravity g . If the point under discussion is shifted to the top of the fluid (say, water), which is open to the atmosphere, P may be replaced by atmospheric pressure (P a ) and we replace P by P. Then Eq.
( . ) gives P = P a + ρ gh ( . ) Thus, the pressure P , at depth below the surface of a liquid open to the atmosphere is greater than atmospheric pressure by an amount ρ gh . The excess of pressure, P − P a , at depth h is called a gauge pressure at that point.
The area of the cylinder is not appearing in the expression of absolute pressure in Eq. ( . ). Thus, the height of the fluid column is important and not cross-sectional or base area or the shape of the container.
The liquid pressure is the same at all points at the same horizontal level (same depth). The result is appreciated through the example of hydrostatic paradox . Consider three vessels A, B and C [Fig. .
] of different shapes. They are connected at the bottom by a horizontal pipe. On filling with water, the level in the three vessels is the same, though they hold different amounts of water. This is so because water at the bottom has the same pressure below each section of the vessel.
Fig . Illustration of hydrostatic paradox. The three vessels A, B and C contain different amounts of liquids, all upto the same height. Example .
What is the pressure on a swimmer m below the surface of a lake? Answer Here h = m and ρ = kg m - . Take g = m s – From Eq. ( .