Exam 15: Fluids

A 12,000-N car is raised using a hydraulic lift, which consists of a U-tube with arms of unequal areas, filled with oil and capped at both ends with tight-fitting pistons. The wider arm of the U-tube has a radius of 18.0 cm and the narrower arm has a radius of 5.00 cm. The car rests on the piston on the wider arm of the U-tube. The pistons are initially at the same level. What is the initial force that must be applied to the smaller piston in order to start lifting the car? For purposes of this problem, neglect the weight of the pistons.

FIGURE 15-2 -Water flows in a pipe as shown in Figure 15-2. The pipe is horizontal at points A and B, then rises in elevation while decreasing in diameter and is again horizontal at points C and D. Vertical tubes, open at the top, are connected to the pipe at A and C, flush with the edge of the pipe. Which of the following statements is correct?

A spar buoy consists of a circular cylinder, which floats with its axis oriented vertically. One such buoy has a radius of 1.00 m, a height of 2.00 m, and weighs 40.0 kN. What portion of it is submerged when it is floating in fresh water?

A piece of aluminum with a mass of 1.0 kg and density of 2700 kg/m³ is suspended from a string and then completely immersed in a container of water. The density of water is 1000 kg/m³. (a) Determine the volume of the piece of aluminum. (b) Determine the tension in the string after the metal is immersed in the container of water.

A barge with vertical sides is 10.0 m wide and 60.0 m long and is floating in fresh water. How much deeper into the water does the barge sink when 300,000 kg of coal are loaded on the barge?

FIGURE 15-7 -The two water reservoirs shown in Figure 15-7 are open to the atmosphere. The manometer contains oil with a density of 820 kg/m³. What is the difference in elevation h if the manometer reading m is 25.0 cm?

Does atmospheric pressure affect the buoyant force on a rigid submarine? Explain why or why not.

In a certain one-lane road there are no entrances or exits. As the road passes through open country and populated areas, the speed limit changes. Assume that cars travel at the posted speed limit. In the open road, where the speed limit is 55 mph, the cars are spaced so there are 51 cars per mile. If the flow of cars is steady, how many cars per mile are there in a stretch of road where the speed limit is 40 mph?

A sphere of radius 10.0 cm floats in equilibrium partially submerged in water with its lowest point 5.00 cm below the water's surface. (a) What is the buoyant force acting on the sphere? (b) What is the weight of the sphere?

In a section of horizontal pipe with a diameter of 3.00 cm the pressure is 100 kPa and water is flowing with a speed of 1.50 m/s. The pipe narrows to 2.00 cm. What is the pressure in the narrower region?

FIGURE 15-4 -The circular pipes shown in Figure 15-4 both contain water, but at different pressures. They are connected by means of an inverted U-tube, which contains oil with a density of 800 kg/m³. The heights are: h_A = 7.0 cm, h_B = 20.0 cm, and h_C = 13.0 cm. What is the pressure difference (P_B - P_A)?

If an external pressure is applied to a confined fluid, the pressure at every point within the fluid increases by that amount.

Two horizontal pipes are the same length, but pipe B has twice the diameter of pipe A. Water undergoes viscous flow in both pipes, subject to the same pressure difference across the lengths of the pipes. If the flow rate in pipe A is Q, what is the flow rate in pipe B?

A rock is suspended from a scale reads 10.0 N. A beaker of water is raised up so the rock is totally submerged in the water. The scale now reads 6.25 N.What is the density of the rock?

Water flows through a pipe. The diameter of the pipe at point B is larger than at point A. Where is the speed of the water greater?

A cylinder, semicircular in cross-section, 10.0 m long and 5.00 m in radius, is completely submerged in water. What is the buoyant force on the cylinder?

A hot air balloon plus its cargo has a mass of 400 kg, and it holds 700 m³ of hot air. It is floating at a constant height in air with a density of 1.29 kg/m³. What is the density of the hot air in the balloon?

A boat loaded with rocks is floating in a swimming pool. If the rocks are thrown into the pool, the water level in the pool, after the rocks have settled to the bottom,

A basketball player pushes down with a force of 50 N on a basketball that is inflated to a gauge pressure of 8.0 x 10⁴ Pa. What is the diameter of contact between the ball and the floor?

Motor oil, with a viscosity of 0.250 Ns/m², is flowing through a tube that has a radius of 5.00 mm and is 25.0 cm long. The drop in pressure is 300 kPa. What is the volume of oil flowing through the tube per unit time?