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What is Bernoulli's Equation?

A statement of energy conservation for fluids, relating pressure, velocity, and height at different points in a flowing fluid: P1+12ρv12+ρgh1=P2+12ρv22+ρgh2P_1 + \frac{1}{2} \rho v_1^2 + \rho g h_1 = P_2 + \frac{1}{2} \rho v_2^2 + \rho g h_2

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What is Bernoulli's Equation?

A statement of energy conservation for fluids, relating pressure, velocity, and height at different points in a flowing fluid: P1+12ρv12+ρgh1=P2+12ρv22+ρgh2P_1 + \frac{1}{2} \rho v_1^2 + \rho g h_1 = P_2 + \frac{1}{2} \rho v_2^2 + \rho g h_2

Define Pressure (P) in the context of fluid dynamics.

Force per unit area. In Bernoulli's equation, it's measured in Pascals (Pa). Higher pressure can push the fluid faster.

What is fluid density (ρ\rho)?

Mass per unit volume of the fluid, typically measured in kg/m³.

Define fluid velocity (v) in Bernoulli's equation.

The speed of the fluid at a given point, measured in m/s. Faster fluid velocity implies more kinetic energy.

What is the definition of Volume flow rate (V)?

The volume of fluid that passes a given point per unit time. It's related to velocity and cross-sectional area by the equation V=vAV = vA.

Define Kinetic Energy in the context of fluid dynamics.

Energy of motion, related to fluid velocity. Faster fluid = more KE.

Define Potential Energy in the context of fluid dynamics.

Energy of position, related to height. Higher fluid = more PE.

What are the differences between Power and Work?

Work: Energy transferred (measured in Joules). Power: Rate of energy transfer (measured in Watts).

In the diagram of a leaking tank, what do the variables represent?

H: Height of the water in the tank, v: Velocity of the water exiting the hole.