The difference in pressure between two points in a fluid system, driving flow from high to low pressure.

A principle stating that for incompressible fluids, the mass flow rate is constant: $A_1v_1 = A_2v_2$.

The mass of fluid passing a point per unit time, given by $\dot{m} = \rho A v$.

An equation expressing conservation of energy in fluid flow: $P_{1}+\rho g y_{1}+\frac{1}{2} \rho v_{1}^{2}=P_{2}+\rho g y_{2}+\frac{1}{2} \rho v_{2}^{2}$.

A theorem stating that the exit velocity of a fluid from a hole is $v=\sqrt{2 g \Delta y}$, where $\Delta y$ is the height difference.

The volume of fluid passing a point per unit time, given by $Q = Av$.

1. Identify two points in the fluid flow. 2. Determine the cross-sectional area and velocity at each point. 3. Apply $A_1v_1 = A_2v_2$ to relate the areas and velocities. 4. Solve for the unknown variable.

1. Identify two points along a streamline. 2. Determine pressure, height, and velocity at each point. 3. Apply $P_{1}+\rho g y_{1}+\frac{1}{2} \rho v_{1}^{2}=P_{2}+\rho g y_{2}+\frac{1}{2} \rho v_{2}^{2}$. 4. Solve for the unknown variable.

1. Identify the height difference between the fluid surface and the exit point. 2. Apply $v = \sqrt{2g\Delta y}$. 3. Solve for the exit velocity, $v$.

Mass flow rate: Mass per unit time ($\rho A v$) | Volume flow rate: Volume per unit time ($A v$)

Gravitational potential energy: Energy due to height, decreases as fluid flows down | Kinetic energy: Energy due to motion, increases as fluid flows down (if potential energy converts to kinetic energy)