Fluid Mechanics — AI Study Guide
Master pressure, buoyancy, fluid flow, and Bernoulli's principle with AI tools from your physics notes.
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Fluid mechanics studies the behavior of fluids (liquids and gases) at rest (fluid statics) and in motion (fluid dynamics). Fluids are substances that cannot permanently resist shear forces and thus flow to fill their container. Pressure in a fluid at rest increases with depth: P = ρgh + P_atm. Pascal's principle states that pressure applied to an enclosed fluid is transmitted unchanged throughout the fluid — the principle behind hydraulic systems.
Buoyancy — the upward force exerted by a fluid on a submerged object — equals the weight of displaced fluid (Archimedes' principle: F_buoy = ρ_fluid × V_displaced × g). An object floats if its density is less than the fluid's density; it sinks if its density is greater. The fraction of a floating object submerged equals the ratio of the object's density to the fluid's density.
The continuity equation for incompressible fluids states that the volume flow rate is constant: A1v1 = A2v2. Where the cross-sectional area is smaller, the fluid velocity is higher, and vice versa. This explains why rivers narrow and accelerate, and why blood flows faster in capillaries than in the aorta (though individual capillary velocities are low, there are many more of them).
Bernoulli's equation relates pressure, velocity, and height in steady, non-viscous, incompressible flow: P + ½ρv² + ρgh = constant. Along a streamline, as velocity increases, pressure decreases. This explains lift generation on airplane wings (faster flow over curved top surface creates lower pressure), the Venturi effect, and the function of carburetors. Viscosity and turbulence complicate real fluid flow beyond the ideal Bernoulli picture.
Frequently Asked Questions: Fluid Mechanics
What is Archimedes' principle?
Archimedes' principle states that the buoyant force on an object submerged in a fluid equals the weight of fluid displaced: F_buoy = ρ_fluid × V_displaced × g. An object floats when the buoyant force equals its weight (density ≤ fluid density). It sinks when weight exceeds buoyant force (density > fluid density). The fraction of a floating object below the surface equals (density of object)/(density of fluid).
What does Bernoulli's equation tell you?
Bernoulli's equation (P + ½ρv² + ρgh = constant) states that for steady, incompressible, non-viscous flow, the sum of static pressure, dynamic pressure (½ρv²), and hydrostatic pressure (ρgh) is constant along a streamline. Practical implication: higher velocity fluid has lower static pressure. This explains airplane lift (higher velocity air over curved wing creates lower pressure above wing), the Venturi meter, and atomizer sprayers.
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