A scuba diver makes a slow descent into the depths of the ocean. His vertical position with respect to a boat on the surface changes several times. He makes the first stop 8.0 m from the boat but has a problem with equalizing the pressure, so he ascends 5.0 m and then continues descending for another 12.0 m to the second stop. From there, he ascends 5.0 m and then descends for 14.0 m, ascends again for 7.0 m and descends again for 12.0 m, where he makes a stop, waiting for his buddy. Assuming the positive direction up to the surface (+ĵ), express his net vertical displacement vector (in m) in terms of the unit vector ĵ. (Express your answer in vector form.)

A manometer containing water with one end connected to a container of gas has a column height difference of 0.60 m (Fig. P15.72). If the atmospheric pressure on the right column is 1.01 105 Pa, find the absolute pressure of the gas in the container. The density of water is 1.0 103 kg/m3. FIGURE P15.72

A manometer is shown in Figure P15.36. Rank the pressures at the five locations indicated from highest to lowest. Indicate equal pressures, if any. FIGURE P15.36

A tank with a flat bottom of area A and vertical sides is filled to a depth h with water. The pressure is P0 at the top surface. (a) What is the absolute pressure at the bottom of the tank? (b) Suppose an object of mass M and density less than the density of water is placed into the tank and floats. No water overflows. What is the resulting increase in pressure at the bottom of the tank?

(a) Calculate the absolute pressure at an ocean depth of 1 000 m. Assume the density of seawater is 1 030 kg/m3 and the air above exerts a pressure of 101.3 kPa. (b) At this depth, what is the buoyant force on a spherical submarine having a diameter of 5.00 m?

Review. In a water pistol, a piston drives water through a large tube of area A1 into a smaller tube of area A2 as shown in Figure P14.46. The radius of the large tube is 1.00 cm and that of the small tube is 1.00 mm. The smaller tube is 3.00 cm above the larger tube. (a) If the pistol is fired horizontally at a height of 1.50 m, determine the time interval required for the water to travel from the nozzle to the ground. Neglect air resistance and assume atmospheric pressure is 1.00 atm. (b) If the desired range of the stream is 8.00 m, with what speed v2 must the stream leave the nozzle? (c) At what speed v1 must the plunger be moved to achieve the desired range? (d) What is the pressure at the nozzle? (e) Find the pressure needed in the larger tube. (f) Calculate the force that must be exerted on the trigger to achieve the desired range. (The force that must be exerted is due to pressure over and above atmospheric pressure.) Figure P14.46

A hollow copper (Cu = 8.92 103 kg/m3) spherical shell of mass m = 0.950 kg floats on water with its entire volume below the surface. a. What is the radius of the sphere? b. What is the thickness of the shell wall?

You are applying for a position with a sea rescue unit and are taking the qualifying exam. One question on the exam is about the use of a diving bell. The diving bell is in the shape of a cylinder with a vertical length of L = 2.50 m. It is closed at the upper circular end and open at the lower circular end. The hell is lowered from air into seawater ( = 1.025 g/cm3) and kept in its upright orientation as it is lowered. The air in the bell is initially at temperature Ti = 20.0C. The bell, with two humans inside, is lowered to a depth (measured to the bottom of the bell) of 27.0 fathoms, or h = 49.4 m. At this depth the water temperature is Tf = 4.0C, and the bell is in thermal equilibrium with the water. The exam question asks you to compare two situations: (i) No additional gas is added to the interior of the bell as it is submerged. Therefore, water enters the open bottom of the bell and the volume of the enclosed air decreases. (ii) The bell is fitted with pressurized air tanks, which deliver high-pressure air into the interior of the bell to keep the level of water at the bottom edge of the bell. This choice requires money and effort to attach the tanks. The exam question asks: Which scenario is better?

The human brain and spinal cord are immersed in the cerebrospinal fluid. The fluid is normally continuous between the cranial and spinal cavities and exerts a pressure of 100 to 200 mm of H2O above the prevailing atmospheric pressure. In medical work, pressures are often measured in units of mm of H2O because body fluids, including the cerebrospinal fluid, typically have nearly the same density as water. The pressure of the cerebrospinal fluid can be measured by means of a spinal tap. A hollow tube is inserted into the spinal column, and the height lo which the fluid rises is observed, as shown in Figure P9.83. If the fluid ruses to a height of 160. mm, we write its gauge pressure as 160. mm H2O. (a) Express this pressure in pascals, in atmospheres, and in millimeters of mercury. (b) Sometimes it is necessary to determine whether an accident victim has suffered a crushed vertebra that is blocking the flow of cerebrospinal fluid in the spinal column. In other cases, a physician may suspect that a tumor or other growth is blocking the spinal column and inhibiting the flow of cerebrospinal fluid. Such conditions ran be investigated by means of the Queckensted test. In this procedure, the veins in the patients neck are compressed lo make the blood pressure rise in the brain. The increase in pressure in the blood vessels is transmitted to the cerebrospinal fluid. What should be the normal effect on the height of the fluid in the spinal tap? (c) Suppose compressing the veins had no effect on the level of the fluid. What might account for this phenomenon?

(a) How high will water rise in a glass capillary tube with a 0.500-mm radius? (b) How much gravitational potential energy does the water gain? (c) Discuss possible sources of this energy.