Exam 10: Fluids

The Tonga Trench in the Pacific Ocean is 36,000 feet deep. Assuming that sea water has an average density of $1.04 \mathrm {~g} / \mathrm { cm } ^ { 3 }$ calculate the absolute (total) pressure at the bottom of the trench in atmospheres. $\left( 1.00 \mathrm { in } = 2.54 \mathrm {~cm} , 1.00 \mathrm {~atm} = 1.01 \times 10 ^ { 5 } \mathrm {~Pa} \right)$

A rectangular wooden block measures $10.0 \mathrm {~cm} \times 4.00 \mathrm {~cm} \times 2.00 \mathrm {~cm}$ When the block is placed in water, it floats horizontally, with its bottom face 1.65 cm below the surface. What is the density of the wood? The density of water is $1.00 \mathrm {~g} / \mathrm { cm } ^ { 3 }$

In a section of horizontal pipe with a diameter of 3.0 cm, the pressure is 100 kPa and water is flowing with a speed of 1.5 m/s. The pipe narrows to 2.0 cm. What is the pressure in the narrower region? Treat the water as an ideal incompressible fluid.

Water flows out of a large reservoir through an open pipe, as shown in the figure. What is the speed of the water as it comes out of the pipe?

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. Assume the pistons each have negligible weight. (a) Determine the force that must be applied to the small piston. (b) Determine the pressure applied to the fluid in the lift.

The bathyscaphe Trieste consists of a thin-walled but very strong cylindrical hull, 15.2 m long and 3.66 m in diameter, filled with gasoline with a density of $880 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ to make it buoyant. If it is totally submerged in seawater with a density of $1025 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ and neither rising nor sinking, what is the weight of the Trieste craft?

A large cylindrical water tank 11.5 m in diameter and 13.5 m tall is supported with its base 8.75 m above the ground by a stand as shown in the figure. The water level in the tank is 10.6 m deep, and the density of the water in the tank is $1.00 \mathrm {~g} / \mathrm { cm } ^ { 3 }$ A very small hole is formed at the base of the vertical wall of the tank, and water is squirting out of this hole horizontally. When this water hits the ground, how far has it traveled horizontally from the hole, assuming no air resistance?

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 with a density of $800 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ 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, neglect the weight of the pistons.

What force does the water exert (in addition to that due to atmospheric pressure) on a submarine window of radius 44.0 cm at a depth of 9400 m in sea water? The density of sea water is 1025 $\mathrm { kg } / \mathrm { m } ^ { 3 }$

A hollow sphere of negligible mass and radius R is completely filled with a liquid so that its density is $\rho$ You now enlarge the sphere so its radius is 2R and completely fill it with the same liquid. What is the density of the enlarged sphere?

A compressed gas with a total mass of 107 kg is stored in a spherical container having a radius of 0.521 m. What is the density of the compressed gas?

A water tank is filled to a depth of 10 m, and the bottom of the tank is 20 m above ground. A water-filled hose that is 2.0 cm in diameter extends from the bottom of the tank to the ground, but no water is flowing in this hose. The water pressure at ground level in the hose is closest to which of the following values? The density of water is $1000 \mathrm {~kg} / \mathrm { m } ^ { 3 }$

In a hydraulic garage lift, the small piston has a radius of 5.0 cm and the large piston has a radius of 15 cm. What force must be applied on the small piston in order to lift a car weighing 20,000 N on the large piston? Assume the pistons each have negligible weight.

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 gauge pressure p on the bottom of this block as a function of time t if the block just enters the water at time t = 0 s?

The density of material at the center of a neutron star is approximately $1.00 \times 10 ^ { 18 } \mathrm {~kg} / \mathrm { m } ^ { 3 }$ What is the mass of a cube of this material that is 1.76 microns on each side. (One micron is equal to $1.00 \times$ $\left. 10 ^ { - 6 } \mathrm {~m} . \right)$

A fluid is flowing with an average speed of 1.5 m/s through a tube that has a radius of 2.0 mm and is 18 cm long. The drop in pressure is 967 Pa. What is the viscosity of the fluid?

A spherical ball of lead $\text { (density } 11.3 \mathrm {~g} / \mathrm { cm } ^ { 3 } \text { ) }$ is placed in a tub of mercury $\left( \text { density } 13.6 \mathrm {~g} / \mathrm { cm } ^ { 3 } \right)$ Which answer best describes the result?

Ideal incompressible fluid flows through a 4.0-cm-diameter pipe at 1.0 m/s . There is a 2.0 cm diameter constriction in the line. What is the speed of the fluid in this constriction?

An ideal incompressible fluid flows at 0.252 m/s through a 44-mm diameter cylindrical pipe. The pipe widens to a square cross sectional area that is 5.5 cm on a side. Assume steady flow throughout the system. (a) What is the speed of the fluid through the square section of pipe? (b) What is the flow rate in liters per minute?

A container has a vertical tube, whose inner radius is 12.00 mm, connected to it at its side, as shown in the figure. An unknown liquid reaches level A in the container and level B in the tube -level A being 5.0 cm higher than level B. The liquid supports a 20-cm high column of oil, between levels B and C , whose density is $320 \mathrm {~kg} / \mathrm { m } ^ { 3 }$ The gauge pressure at level B is closest to