Unit: Fluids

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In a static (at rest) fluid, pressure increases with depth. Deeper layers support the weight of all fluid above them.

Consider a horizontal surface at depth hh below the fluid surface. The fluid column above has height hh and cross-sectional area AA.

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The volume of the fluid column is

V=AhV = A h

Since density is ρ=m/V\rho = m/V, the mass of this column is

m=ρV=ρAhm = \rho V = \rho A h

The weight of the column acts downward on the surface:

F=mg=ρAhgF = m g = \rho A h g

Pressure is force per unit area. Dividing by AA:

P=FA=ρAhgA=ρghP = \frac{F}{A} = \frac{\rho A h g}{A} = \rho g h

This is the hydrostatic pressure formula:

P=ρghP = \rho g h

Here ρ\rho is fluid density, gg is gravitational acceleration, and hh is depth. This assumes an incompressible, static fluid.

A key insight: pressure depends only on depth. The container shape and total fluid volume do not matter. At depth hh, the pressure P=ρghP = \rho g h acts equally in all directions—on floors, walls, and any submerged object.

... continued in the full lesson.

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