Exam 14: Fluids and Elasticity

A steel lift column in a service station is a solid cylinder 4.0 m long and 0.20 m in diameter. Young's modulus for this steel is 20 × 10¹⁰ N/m². By what distance does the column compress when a 5000-kg truck is on it?

Incompressible water flows out of a large reservoir through a pipe that opens to the atmosphere 5.70 m below the level of the water in the reservoir. What is the speed of the water as it comes out of the pipe?

Water flows in the horizontal pipe shown in the figure. At A, the diameter is 5.00 cm, and at B, the diameter is 4.00 cm. The fluid in the manometer is mercury, which has a density of 13,600 kg/m³. The manometer reading h is 4.40 cm. We can treat water as an ideal fluid having a density of 1000 kg/m³. What volume of water is flowing through the pipe per second?

The small piston of a hydraulic lift has a diameter of 8.0 cm, and its large piston has a diameter of 40 cm. The lift raises a load of 15,000 N. (a) Determine the force that must be applied to the small piston. (b) Determine the pressure applied to the fluid in the lift.

What is the radius of a sphere that has a density of 5000 kg/m³ and a mass of 6.00 kg?

A large cylindrical water tank is mounted on a platform with its central axis vertical. The water level is 3.75 m above the base of the tank, and base is 6.50 m above the ground. A small hole 2.22 mm in diameter has formed in the base of the tank. Both the hole and the top of the tank are open to the air. We can ignore air resistance and treat water as an ideal fluid with a density of 1000 kg/m³. (a) How many cubic meters of water per second is this tank losing? (b) How fast is the water from the hole moving just as it reaches the ground?

The two water reservoirs shown in the figure are open to the atmosphere, and the water has density 1000 kg/m³. The manometer contains incompressible mercury with a density of 13,600 kg/m³. What is the difference in elevation h if the manometer reading m is 25.0 cm?

A piece of wood is floating in a bathtub. A second piece of wood sits on top of the first piece, and does not touch the water. If the top piece is taken off and placed in the water, what happens to the water level in the tub?

A 0.600-mm diameter wire stretches 0.500% of its length when it is stretched with a tension of 20.0 N. What is the Young's modulus of this wire?

A steel rod 55 cm long has a diameter of 30 cm. The compressive strength (the maximum stress it can support without breaking) of this steel is 500 × 10⁶ N/m². What is the compression force that would break the rod?

A cable is 100 m long, has a cross-sectional area of 1.0 mm², and is made of a material having a Young's modulus of 1.0 × 10¹¹ N/m². If a 1000-N force is applied to stretch the cable, how far does it stretch?

A 12,000-N car is raised using a hydraulic lift, which consists of a U-tube with arms of unequal areas, filled with incompressible oil with a density of 800 kg/m³ 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 force that must be applied to the smaller piston in order to lift the car after it has been raised 1.20 m? (For purposes of this problem, you can neglect the weight of the pistons.)

A 12-L volume of oil is subjected to a pressure change, which produces a volume strain on the oil of -3.0 × 10^-4. The bulk modulus of the oil is 6.0 × 10⁹ N/m² and is independent of the pressure. What is the pressure change that produced the volume strain in the oil?

A 7.8-kg solid sphere, made of metal whose density is 2500 kg/ , is suspended by a cord. When the sphere is immersed in water (of density 1000 kg/m³), what is the tension in the cord?

A paint sprayer pumps air through a constriction in a 2.50-cm diameter pipe, as shown in the figure. The flow causes the pressure in the constricted area to drop and paint rises up the feed tube and enters the air stream. The speed of the air stream in the 2.50-cm diameter sections is 5.00 m/s. The density of the air is 1.29 kg/m³, and the density of the paint is 1200 kg/m³. We can treat the air and paint as incompressible ideal fluids. What is the maximum diameter of the constriction that will allow the sprayer to operate?

The weight of a car of mass 1.20 × 10³ kg is supported equally by the four tires, which are inflated to the same gauge pressure. What gauge pressure in the tires is required so the area of contact of each tire with the road is 1.00 × 10² cm²? (1 atm = 1.01 × 10⁵ Pa.)

A person who weighs 550 N empties her lungs as much as possible and is then completely immersed in water (of density 1000 kg/m³) while suspended from a harness. Her apparent weight is now 21.2 N. What is her density?

A 12,000-N car is raised using a hydraulic lift, which consists of a U-tube with arms of unequal areas, filled with incompressible 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, you can neglect the weight of the pistons.)

Water flows in the horizontal pipe shown in the figure. At point A the area is 25.0 cm² and the speed of the water is At B the area is 16.0 cm². The fluid in the manometer is mercury, which has a density of 13,600 kg/m³. We can treat water as an ideal fluid having a density of 1000 kg/m³. What is the manometer reading h?

Fluid fills the container shown in the figure. At which of the indicated points is the pressure greatest?