# Test Prep for AP® Courses

### 12.1 Flow Rate and Its Relation to Velocity

Water flows through a small horizontal pipe with a speed of 12 m/s into a larger part of the pipe for which the diameter of the pipe is doubled. What is the speed of the water in the larger part of the pipe?

- 0.75 m/s
- 3 m/s
- 6 m/s
- 12 m/s

A popular pool toy allows the user to push a plunger to compress water in a barrel with a diameter of 3 cm. The water is compressed with a speed of 1.2 m/s and emerges from a small opening with a speed of 15 m/s. What is the diameter of the opening? Assume the toy is oriented horizontally.

### 12.2 Bernoulli’s Equation

At what depth beneath the surface of the lake is the pressure in the water equal to twice atmospheric pressure?

- 10 m
- 100 m
- 1,000 m
- 10,000 m

A pump provides pressure to the lower end of a long pipeline that supplies water from a reservoir to a house located on a hill 150 m vertically upward from the lower end of the pipe where the water is initially at rest before being pumped. The pipeline has a constant diameter of 3.5 cm, and the upper end of the pipeline is open to the atmosphere. What pressure must the pump provide for water to flow from the upper end of the pipeline at a rate of 5 m/s?

According to Bernoulli's equation, if the pressure in a given fluid is constant and the kinetic energy per unit volume of a fluid increases, which of the following is true?

- The potential energy per unit volume of the fluid decreases.
- The potential energy per unit volume of the fluid increases.
- The fluid must no longer be considered incompressible.
- The flow rate of the fluid increases.

Consider the following circumstances within a fluid, and determine the answer using Bernoulli's equation. (a) The pressure and kinetic energy per unit volume along a fluid path increases. What must be true about the potential energy per unit volume of the fluid along the fluid path? Explain. (b) The pressure along a fluid path increases, and the kinetic energy per unit volume remains constant. What must be true about the potential energy per unit volume of the fluid along the fluid path? Explain.

### 12.3 The Most General Applications of Bernoulli’s Equation

A horizontally oriented pipe has a diameter of 5.6 cm and is filled with water. The pipe draws water from a reservoir that is initially at rest. A manually operated plunger provides a force of 440 N in the pipe. Assuming that the other end of the pipe is open to the air, with what speed does the water emerge from the pipe?

- 12 m/s
- 19 m/s
- 150 m/s
- 190 m/s

A 3.5-cm-diameter pipe contains a pumping mechanism that provides a force of 320 N to push water up into a tall building. Upon entering the piston mechanism, the water is flowing at a rate of 2.5 m/s. The water is then pumped to a level 21 m higher where the other end of the pipe is open to the air. With what speed does water leave the pipe?

A large container of water is open to the air, and it develops a hole of area 10 cm^{2} at a point 5 m below the surface of the water. What is the flow rate (m^{3}⁄s) of the water emerging from this hole?

- 99 m
^{3}⁄s - 9.9 m
^{3}⁄s - 0.099 m
^{3}⁄s - 0.0099 m
^{3}⁄s

A pipe is tapered so that the large end has a diameter twice as large as the small end. What must be the gauge pressure, the difference between pressure at the large end and pressure at the small end, in order for water to emerge from the small end with a speed of 12 m/s if the small end is elevated 8 m above the large end of the pipe?