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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: $P_1 + \frac{1}{2} \rho v_1^2 + \rho g h_1 = P_2 + \frac{1}{2} \rho v_2^2 + \rho g h_2$
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 ($\rho$)?
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 $V = vA$.
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 is the effect of increasing fluid velocity in a horizontal pipe, according to Bernoulli's principle?
A decrease in pressure.
What happens to fluid velocity when a pipe narrows, assuming constant volume flow rate?
The fluid velocity increases.
What is the effect of increasing the height of a fluid on its potential energy?
The potential energy increases.
What happens to the exit velocity of water from a hole in a tank if the water height is increased?
The exit velocity increases (specifically, $v = \sqrt{2gh}$).
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.