Water is circulating through a closed system of pipes in a two-floor apartment. On the first floor, the water has a gauge pressure of 3.1 105 Pa and a speed of 2.4 m/s. However, on the second floor, which is 3.8 m higher, the speed of the water is 3.6 m/s. The speeds are different because the pipe diameters are different. What is the gauge pressure of the water on the second floor? Number Units Pa

How tall must a water-filled manometer be to measure blood pressures as high as 300 mm Hg?

(a) A water hose 2.00 cm in diameter is used to fill a 20.0-L bucket. If it takes 1.00 min to fill the bucket, what is the speed v at which water moves through the hose? (Note: 1 L = 1 000 cm3.) (b) The hose has a nozzle 1.00 cm in diameter. Find the speed of the water at the nozzle.

Water flows through a pipe that gradually descends from a height of 6.78 m to the ground. Near the top, the cross-sectional area is 0.400 m2, and the pipe gradually widens so that its area near the ground is 0.800 m2. Water leaves the pipe at a speed of 16.8 m/s. What is the difference in the water pressure between the top and bottom of the pipe?

A spherical submersible 2.00 m in radius, armed with multiple cameras, descends under water in a region of the Atlantic Ocean known for shipwrecks and finds its first shipwreck at a depth of 1.75 103 m. Seawater has density 1.03 103 kg/m3, and the air pressure at the oceans surface is 1.013 105 Pa. a. What is the absolute pressure at the depth of the shipwreck? b. What is the buoyant force on the submersible at the depth of the shipwreck?

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 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) 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.

Fluid originally flows through a tube at a rate of 100 cm3/s. To illustrate the sensitivity of flow rate to various factors, calculate the new flow rate for the following changes with all other factors remaining the same as in the original conditions. (a) Pressure difference increases by a factor of 1.50. (b) A new fluid with 3.00 times greater viscosity is substituted. (c) The tube is replaced by one having 4.00 times the length. (d) Another tube is used with a radius 0.100 times the original. (e) Yet another tube is substituted with a radius 0.100 times the original and half the length, and the pressure difference is increased by a factor of 1.50.

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 millimeters of H2O because body fluids, including the cerebrospinal fluid, typically have the same density as water. The pressure of the cerebrospinal fluid can be measured by means of a spinal tap as illustrated in Figure P14.8. A hollow tube is inserted into the spinal column, and the height to which the fluid rises is observed. If the fluid rises 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) Some conditions that block or inhibit the flow of cerebrospinal fluid can be investigated by means of Queckenstedts test. In this procedure, the veins in the patients neck are compressed to make the blood pressure rise in the brain, which in turn should be transmitted to the cerebrospinal fluid. Explain how the level of fluid in the spinal tap can be used as a diagnostic tool for the condition of the patients spine. Figure P14.8