Exam 11: Fluid Mechanics

Consider a very small hole in the bottom of a tank 20.0 cm in diameter filled with water to a height of 50.0 cm. Find the speed at which the water exits the tank through the hole.

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

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.)

A rock is under water in a shallow lake. As the rock sinks deeper and deeper into water, the buoyant force on it

A horizontal tube consists of a 7.0-cm-diameter pipe that narrows to a 2.0-cm-diameter throat. In the pipe, the water pressure is twice atmospheric pressure and the water flows with a speed of 0.40 m/s. What is the pressure in the throat, assuming that the water behaves like an ideal fluid? The density of water is 1000 kg/m³, and atmospheric pressure is 1.01 × 10⁵ Pa.

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?

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?

A certain coin has a diameter of 21.21 mm, a thickness of 1.95 mm, and weighs 0.04905 N. What is its density?

A sphere is constructed of two concentric parts. The inner part is a solid sphere of radius 10.0 cm made of a material with density 4000 kg/m³. The outer part is a spherical shell with inner radius 10.0 cm and outer radius 20.0 cm. The material in the outer shell has a density 9000 kg/m³. (a) What is the mass of the sphere? (b) What is the average density of this sphere?

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.)