Fluid Mechanics

Hydrostatic Pressure

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Variables:

Description/Usage:

Pressure in a static fluid increases linearly with depth. This is why deep water has higher pressure. For example, every 10 m of water adds about 1 atmosphere of pressure.

Buoyant Force (Archimedes’ Principle)

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Variables:

Description/Usage:

Any object in a fluid experiences an upward force equal to the weight of fluid it displaces. This principle explains floating: if \(F_b\) equals the object’s weight, it floats (weight of displaced fluid = weight of object).

Equation of Continuity

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Variables:

• \(A_1, A_2 are cross-sectional areas of a flow tube at two locations, v_1, v_2 are fluid speeds at those locations (for an incompressible fluid).\)

Description/Usage:

Expresses mass conservation in steady flow: the volume flow rate \(A v\) is constant along a streamline. If a pipe narrows (smaller \(A\)), the fluid speed \(v\) increases.