A scuba diver jumps into the water to inspect the capsized Costa Concordia cruise ship that ran aground off the west coast of Italy at Giglio island January 16, 2012. Max Rossi

A diver descends from a salvage ship to the ocean floor at a depth of 35 m below the surface. The density of ocean water is 1.025 x 10^{3} kg/m^{3}.

(a) Calculate the gauge pressure on the diver on the ocean floor*.*

(b) Calculate the absolute pressure on the diver on the ocean floor.

The diver finds a rectangular aluminum plate having dimensions 1.0 m x 2.0 m x0.03 m. A hoisting cable is lowered from the ship and the diver connects it to the plate. The density of aluminum is 2.7 x103 kg/m^{3}. Ignore the effects of viscosity.

(c) Calculate the tension in the cable if it lifts the plate upward at a slow, constant velocity.

(d) Will the tension in the hoisting cable increase, decrease, or remain the same if the plate accelerates upward at 0.05 m/s^{2}?

____ increase ____ decrease ____ remain the same

Explain your reasoning.

A fountain with an opening of radius 0.015 m shoots a stream of water vertically from ground level at 6.0 m/s.

The density of water is 1000 kg/m^{3}.

(a) Calculate the volume rate of flow of water.

(b) The fountain is fed by a pipe that at one point has a radius of 0.025 m and is 2.5 m below the fountain’s opening. Calculate the absolute pressure in the pipe at this point.

(c) The fountain owner wants to launch the water 4.0 m into the air with the same volume flow rate. A nozzle can be attached to change the size of the opening. Calculate the radius needed on this new nozzle.

A 20 m high dam is used to create a large lake. The lake is filled to a depth of 16 m as shown above. The density of water is 1000 kg/m^{3} .

(a) Calculate the absolute pressure at the bottom of the lake next to the dam.

A release valve is opened 5.0 m above the base of the dam, and water exits horizontally from the valve.

(b) Use Bernoulli’s equation to calculate the initial speed of the water as it exits the valve.

(c) The stream below the surface of the dam is 2.0 m deep. Assuming that air resistance is negligible, calculate the horizontal distance *x *from the dam at which the water exiting the valve strikes the surface of the stream.

(d) Suppose that the atmospheric pressure in the vicinity of the dam increased. How would this affect the initial speed of the water as it exits the valve?

___It would increase. ____It would decrease. ____It would remain the same.

Justify your answer.

An underground pipe carries water of density 1000 kg/m^{3} to a fountain at ground level, as shown above. At point *A*, 0.50 m below ground level, the pipe has a cross-sectional area of 1.0 x 10^{-4} m^{2}. At ground level, the pipe has a cross-sectional area of 0.50 x 10^{-4} m^{2}. The water leaves the pipe at point *B *at a speed of 8.2 m/s.

(a) Calculate the speed of the water in the pipe at point *A*.

(b) Calculate the absolute water pressure in the pipe at point *A*.

(c) Calculate the maximum height above the ground that the water reaches upon leaving the pipe vertically at ground level, assuming air resistance is negligible.

(d) Calculate the horizontal distance from the pipe that is reached by water exiting the pipe at 60° from the level ground, assuming air resistance is negligible.

In the laboratory, you are given a cylindrical beaker containing a fluid and you are asked to determine the density *ρ *of the fluid. You are to use a spring of negligible mass and unknown spring constant k attached to a stand. An irregularly shaped object of known mass *m *and density *D *(D >> *ρ*) hangs from the spring. You may also choose from among the following items to complete the task.

- A metric ruler
- A stopwatch
- String

(a) Explain how you could experimentally determine the spring constant *k*.

(b) The spring-object system is now arranged so that the object (but none of the spring) is immersed in the unknown fluid, as shown. Describe any changes that are observed in the spring-object system and explain why they occur.

(c) Explain how you could experimentally determine the density of the fluid.

(d) Show explicitly, using equations, how you will use your measurements to calculate the fluid density *ρ*. Start by identifying any symbols you use in your equations.