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Describe the steps to solve a changing pipe radius problem.
1. Relate area to radius ($A = \pi r^2$). 2. Determine area change based on radius change. 3. Apply constant flow rate principle. 4. Calculate the new velocity.
What is the effect of increasing the radius of a pipe on the fluid velocity, assuming constant flow rate?
Increasing the radius decreases the fluid velocity.
What happens to the flow rate if mass is added to a closed system?
If mass is added to the system, the flow rate increases.
What is the effect of decreasing the cross-sectional area of a pipe on the fluid velocity?
Decreasing the cross-sectional area increases the fluid velocity.
What happens to the pressure if the fluid velocity increases in a horizontal pipe?
The pressure decreases.
What is the effect of pumping water into a tank at the same rate it's pumped out, assuming constant temperature?
The mass flow rate remains constant.
Define flow rate (f).
Flow rate (f) is the speed of the fluid (v) multiplied by the cross-sectional area (A): $f = vA$
What is the continuity equation?
The continuity equation states that the flow rate is constant at any two points in a pipe: $A_1v_1 = A_2v_2$
Define mass flow rate.
Mass flow rate is the mass of fluid passing through a system per unit time.
What is the mathematical expression for mass conservation in fluids?
The sum of mass flow rates entering the system equals the sum of mass flow rates leaving the system: $\Sigma \dot{m}_{in} = \Sigma \dot{m}_{out}$
What is the relationship between area, velocity, and pressure in fluid dynamics?
Larger area = smaller velocity = larger pressure; Smaller area = larger velocity = smaller pressure