Exam 10: Fluids

A crane lifts a steel submarine of density $7800 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ and mass 20,000 kg. What is the tension in the lifting cable (a) when the submarine is submerged in water of density $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ and (b) when it is entirely out of the water?

A cylinder, semicircular in cross-section, is 10 m long and 5.0 m in radius. It is completely submerged, with its flat bottom side horizontal and 8.0 m below the water surface, as shown in the figure. What is the magnitude of the net force on the curved upper surface of the half-cylinder? Neglect atmospheric pressure.

A 200-N object floats with three-fourths of its volume beneath the surface of the water. What is the buoyant force on the object? The density of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

A hole of radius 1.0 mm forms in the bottom of a very large water storage tank that holds water to a depth of 15 m. At what volume rate will water flow out of the hole?

A wooden raft has a mass of 55 kg. When empty it floats in water $\text { (density } 1000 \mathrm {~kg} / \mathrm { m } ^ { 3 } \text { ) }$ with 64% of its volume submerged. What maximum mass of sand can be put on the raft without sinking it?

A 500-N weight sits on the small piston of a hydraulic machine. The small piston has an area of $2.0 \mathrm {~cm} ^ { 2 }$ If the large piston has an area of $40 \mathrm {~cm} ^ { 2 }$ how much weight can the large piston support? Assume the pistons each have negligible weight.

An ideal incompressible fluid flows at 12 m/s in a horizontal pipe. If the pipe widens to twice its original radius, what is the flow speed in the wider section?

A cubical block of stone is lowered at a steady rate into the ocean by a crane, always keeping the top and bottom faces horizontal. Which one of the following graphs best describes the buoyant force B on this block as a function of time t if the block just enters the water at time t = 0 s?

A cubical box 25.0 cm on each side is immersed in a fluid. The pressure at the top surface of the box is 109.40 kPa and the pressure on the bottom surface is 112.00 kPa. What is the density of the fluid?

Fluid flows at 2.0 m/s through a pipe of diameter 3.0 cm. What is the volume flow rate of the fluid?

A round coin has a diameter of 19.55 mm , a thickness of 1.55 mm , and a mass of 2.50 g. What is its density?

The weight of a 1200-kg car is supported equally by the four tires, which are inflated to the same gauge pressure. What gauge pressure is required so the area of contact of each tire with the road is $100 \mathrm {~cm} ^ { 2 } ?$

Calculate the pressure exerted on the ground due to the weight of a 79-kg person standing on one foot. if the bottom of the person's foot is 13 cm wide and 28 cm long.

Water flows through a horizontal pipe of cross-sectional area $10.0 \mathrm {~cm} ^ { 2 }$ at a pressure of 0.250 atm with a flow rate is 1.00 L/s. At a valve, the effective cross-sectional area of the pipe is reduced to $5.00 \mathrm {~cm} ^ { 2 }$ What is the pressure at the valve? The density of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ , and treat it as an ideal incompressible fluid.

Motor oil, with a viscosity of $0.25 \mathrm {~N} \cdot \mathrm { s } / \mathrm { m } ^ { 2 }$ is flowing through a tube that has a radius of 3.0 mm and is 1.0 m long. The drop in pressure over the length of the tube is 200 kPa. What is the average speed of the oil?

When a heavy metal block is supported by a cylindrical vertical post of radius R, it exerts a force F on the post. If the diameter of the post is increased to 2R , what force does the block now exert on the post?

A pressurized cylindrical tank, 5.0 m in diameter, contains water that emerges from the pipe at point C with a speed of 84 m/s, as shown in the figure. Point A is 10 m above point B and point C is 3.0 m above point B. The area of the pipe at point B is $0.080 \mathrm {~m} ^ { 2 }$ and the pipe narrows to an area of $0.070 \mathrm {~m} ^ { 2 }$ at point C. Assume that the water is an ideal fluid in laminar flow. The density of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ The rate at which the water level is falling in the tank is closest to

An object weighs 7.84 N when it is in air and 6.86 N when it is immersed in water of density 1000 $\mathrm { kg } / \mathrm { m } ^ { 3 }$ What is the density of the object?

A person who weighs 550 N empties her lungs as much as possible and is then completely immersed in water of density $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ while suspended from a harness. Her apparent weight is now 21.2 N. What is her density?

When a box rests on a round sheet of wood on the ground, it exerts an average pressure $p$ on the wood. If the wood is replaced by a sheet that has half the diameter of the original piece, what is the new average pressure?