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What are the general steps to solve problems using Bernoulli's Equation?
1. Identify two points in the fluid flow. 2. List knowns and unknowns (P, v, h) at each point. 3. Simplify the equation by canceling out negligible terms. 4. Plug in values and solve for the unknown.
How do you apply the Continuity Equation in fluid dynamics problems?
1. Identify two points in the fluid flow where the cross-sectional area changes. 2. Use the equation $V = vA$ (volume flow rate = velocity * area) to relate the velocities at the two points. 3. If the volume flow rate is constant, then $v_1A_1 = v_2A_2$.
How do you solve a leaking tank problem using Bernoulli's equation?
1. Recognize that the velocity at the top of the tank is negligible ($v_1 \approx 0$). 2. Recognize that both the top and the leak are at atmospheric pressure ($P_1 = P_2$). 3. Simplify Bernoulli's equation to $\rho g h = \frac{1}{2} \rho v^2$. 4. Solve for the velocity of the leak: $v = \sqrt{2gh}$
What are the steps to calculate the work done by a pump moving water to a certain height?
1. Calculate the potential energy change: $\Delta PE = mgh = V\rho g \Delta h$. 2. Recognize that the work done by the pump equals the change in potential energy of the water. 3. Use the power equation: $W = Pt$, so $t = W/P = \Delta PE/P$. 4. Calculate the time and then the work done: $W = P*t$.
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.
What are the differences between Power and Work?
Work: Energy transferred (measured in Joules). Power: Rate of energy transfer (measured in Watts).