Chapter 13

Water flows through a hose of diameter \(3.90 \mathrm{~cm}\) at a velocity of \(5.00 \mathrm{~m} / \mathrm{s}\). Find the flow rate of the hose in \(\mathrm{L} / \mathrm{min}\).

A metal alloy weighs \(81.0 \mathrm{lb}\) in air and \(68.0 \mathrm{lb}\) when under water. Find the buoyant force of the water.

The area of the small piston in a hydraulic jack is \(0.750 \mathrm{in}^{2} .\) The area of the large piston is \(3.00 \mathrm{in}^{2} .\) If a force of \(15.0 \mathrm{lb}\) is applied to the small piston, what weight can be lifted by the large one?

Find the pressure (in \(\mathrm{lb} / \mathrm{in}^{2}\) ) at the bottom of a tower with water \(50.0 \mathrm{ft}\) deep.

Water flows through a \(15.0-\mathrm{cm}\) fire hose at a rate of \(5.00 \mathrm{~m} / \mathrm{s}\). (a) Find the rate of flow through the hose in L/min. (b) How many litres pass through the hose in \(30.0\) min?

A piece of metal weighs \(67.0 \mathrm{~N}\) in air and \(62.0 \mathrm{~N}\) in water. Find the buoyant force of the water.

Change \(64.3 \mathrm{lb} / \mathrm{in}^{2}\) to \(\mathrm{kPa}\).

The mechanical advantage of a hydraulic press is \(25 .\) What applied force is necessary to produce a pressing force of \(2400 \mathrm{~N}\) ?

Find the height of a column of water where the pressure at the bottom of the column is \(20.0 \mathrm{lb} / \mathrm{in}^{2}\).

Water flows from a pipe at \(650 \mathrm{~L} / \mathrm{min} .\) (a) What is the diameter (in \(\mathrm{cm}\) ) of the pipe if the velocity of the water is \(1.5 \mathrm{~m} / \mathrm{s}\) ? (b) Find the velocity (in \(\mathrm{m} / \mathrm{s}\) ) of the water if the diameter of the pipe is \(20.0 \mathrm{~cm}\).

A rock weighs \(25.7 \mathrm{~N}\) in air and \(21.8 \mathrm{~N}\) in water. What is the buoyant force of the water?

Change \(42.5 \mathrm{lb} / \mathrm{in}^{2}\) to \(\mathrm{kPa}\).

Find the mechanical advantage of a hydraulic press that produces a pressing force of \(8250 \mathrm{~N}\) when the applied force is \(375 \mathrm{~N}\).

Water flows through a pipe of diameter \(8.00 \mathrm{~cm}\) at \(45.0 \mathrm{~m} / \mathrm{min}\). Find the flow rate (a) in \(\mathrm{m}^{3} / \mathrm{min}\) and (b) in \(\mathrm{L} / \mathrm{s}\).

A metal bar weighs \(455 \mathrm{~N}\) in air and \(437 \mathrm{~N}\) in water. What is the buoyant force of the water?

Change \(215 \mathrm{kPa}\) to \(\mathrm{lb} / \mathrm{in}^{2}\).

The mechanical advantage of a hydraulic press is 18 . What applied force is necessary to produce a pressing force of \(990 \mathrm{lb}\) ?

(a) Find the total force on the bottom of a water-filled circular cattle tank \(0.750 \mathrm{~m}\) high with radius \(1.30 \mathrm{~m}\) where the weight density of water is \(98 \overline{0} 0 \mathrm{~N} / \mathrm{m}^{3}\). (b) Find the total force on the side of the tank.

A pump is rated to deliver \(50.0\) gal/min. Find the velocity of water in (a) a 6.00-in.-diameter pipe and (b) a 3.00-in.-diameter pipe.

Find the pressure of (a) 3 atm (in \(\mathrm{kPa}\) ), (b) \(2 \mathrm{~atm}\) (in \(\mathrm{kPa}\) ), (c) \(6 \mathrm{~atm}\) (in \(\mathrm{lb} / \mathrm{in}^{2}\) ), (d) 5 atm (in \(\mathrm{kPa}\) ), (e) \(\frac{1}{3}\) atm (in \(\mathrm{kPa}\) ), and (f) \(\frac{1}{4}\) atm (in \(\mathrm{kPa}\) ).

Find the mechanical advantage of a hydraulic press that produces a pressing force of \(1320 \mathrm{~N}\) when the applied force is \(55.0 \mathrm{~N}\).

What must the water pressure be to supply water to the third floor of a building (35.0 ft up) with a pressure of \(40.0 \mathrm{lb} / \mathrm{in}^{2}\) at that level?

What size pipe needs to be attached to a pump rated at \(36.0 \mathrm{gal} / \mathrm{min}\) if the desired velocity is \(10.0 \mathrm{ft} / \mathrm{min}\) ? Give the inner diameter in inches.

A metal displaces \(16.8 \mathrm{~m}^{3}\) of water. Find the buoyant force of the water.

A barometer in the Rocky Mountains reads \(516 \mathrm{~mm}\) of mercury. Find this pressure (a) in \(\mathrm{kPa}\) and \((\mathrm{b})\) in \(\mathrm{lb} / \mathrm{in}^{2}\).

The small piston of a hydraulic press has an area of \(8.00 \mathrm{~cm}^{2}\). If the applied force is \(25.0 \mathrm{~N}\), find the area of the large piston to exert a pressing force of \(36 \overline{0} 0 \mathrm{~N}\).

A small rectangular tank \(5.00\) in. by \(9.00\) in. is filled with mercury. (a) If the total force on the bottom of the tank is \(165 \mathrm{lb}\), how deep is the mercury? (Weight density of mercury \(=0.490 \mathrm{lb} / \mathrm{in}^{3} .\) ) (b) Find the total force on the larger side of the tank.

The MA of a hydraulic jack is \(250 .\) What force must be applied to lift an automobile weighing \(12,000 \mathrm{~N} ?\)

Find the water pressure (in \(\mathrm{kPa}\) ) at the \(25.0\) -m level of a water tower containing water \(50.0 \mathrm{~m}\) deep.

A garden hose is used to fill a bucket in \(30.0 \mathrm{~s}\). If you cover part of the hose nozzle so the speed of the water leaving the hose doubles, how long does it take to fill the bucket?

The small piston of a hydraulic press has an area of \(4.00 \mathrm{in}^{2}\). If the applied force is \(10.0 \mathrm{lb}\), what must the area of the large piston be to exert a pressing force of \(865 \mathrm{lb} ?\)

A liquid flows through a pipe with a diameter of \(0.50 \mathrm{~m}\) at a speed of \(4.20 \mathrm{~m} / \mathrm{s}\). What is the rate of flow in \(\mathrm{L} / \mathrm{min} ?\)

The MA of a hydraulic jack is 420 . Find the weight of the heaviest automobile that can be lifted by an applied force of \(55 \mathrm{~N}\).

A pipe system with a radius of \(0.060 \mathrm{~m}\) has a liquid flowing through it at a speed of \(3.96 \mathrm{~m} / \mathrm{s}\). What is the rate of flow in \(\mathrm{L} / \mathrm{min}\) ?

A metal cylinder displaces \(515 \mathrm{~cm}^{3}\) of gasoline. Find the buoyant force of the gasoline.

Find the gauge pressure of a tire with an absolute pressure of \(425 \mathrm{kPa}\).

The mechanical advantage of a hydraulic jack is \(450 .\) Find the weight of the heaviest automobile that can be lifted by an applied force of \(60.0 \mathrm{~N}\).

The pistons of a hydraulic press have radii of \(2.00 \mathrm{~cm}\) and \(12.0 \mathrm{~cm}\), respectively. (a) What force must be applied to the smaller piston to exert a force of \(5250 \mathrm{~N}\) on the larger? (b) What is the pressure (in \(\mathrm{N} / \mathrm{cm}^{2}\) ) on each piston? (c) What is the mechanical advantage of the press?

The small circular piston of a hydraulic press has an area of \(8.00 \mathrm{~cm}^{2} .\) If the applied force is \(25.0 \mathrm{~N}\), what must the area of the large piston be to exert a pressing force of \(3650 \mathrm{~N}\) ?

A flat-bottom river barge is \(30.0 \mathrm{ft}\) wide, \(85.0 \mathrm{ft}\) long, and \(15.0 \mathrm{ft}\) deep. (a) How many \(\mathrm{ft}^{3}\) of water will it displace while the top stays \(3.00 \mathrm{ft}\) above the water? (b) What load in tons will the barge contain under these conditions if the empty barge weighs \(16 \overline{0}\) tons in dry dock?

Find the gauge pressure of a tank whose absolute pressure is \(1275 \mathrm{kPa}\).

The large piston on a hydraulic lift has radius \(40.0 \mathrm{~cm} .\) The small piston has radius \(5.00 \mathrm{~cm}\) to which a force of \(75.0 \mathrm{~N}\) is applied. (a) Find the force exerted by the large piston. (b) Find the pressure on the large piston. (c) Find the pressure on the small piston. (d) Find the mechanical advantage of the lift. (e) What happens when the area of the small piston is half as large? (f) What happens when the radius of the small piston is half as large?

What must the water pressure be to supply the second floor (18.0 ft up) with a pressure of \(50.0 \mathrm{lb} / \mathrm{in}^{2}\) at that level?

A flat-bottom river barge is \(12.0 \mathrm{~m}\) wide, \(30.0 \mathrm{~m}\) long, and \(6.00 \mathrm{~m}\) deep. (a) How many \(\mathrm{m}^{3}\) of water will it displace while the top stays \(1.00 \mathrm{~m}\) above the water? (b) What load (in newtons) will the barge contain under these conditions if the empty barge weighs \(3.55 \times 10^{6} \mathrm{~N}\) in dry dock?

In a hydraulic system a 20.0-N force is applied to the small piston with crosssectional area \(25.0 \mathrm{~cm}^{2}\). What weight can be lifted by the large piston with crosssectional area \(50.0 \mathrm{~cm}^{2}\) ?

Find the water pressure at ground level to supply water to the third floor of a building \(8.00 \mathrm{~m}\) high with a pressure of \(325 \mathrm{kPa}\) at the third-floor level.

What is the volume (in \(\mathrm{m}^{3}\) ) of the water displaced by a submerged air tank that is acted on by a buoyant force of \(7.50 \times 10^{4} \mathrm{~N}\) ?

What pressure must a pump supply to pump water up to the 30 th floor of a skyscraper with a pressure of \(25 \mathrm{lb} / \mathrm{in}^{2} ?\) Assume that the pump is located on the first floor and that there are \(16.0 \mathrm{ft}\) between floors.

If a dentist's chair weighs \(16 \overline{0} 0 \mathrm{~N}\) and is raised by a large piston with crosssectional area \(75.0 \mathrm{~cm}^{2}\), what force must be exerted on a small piston of crosssectional area \(3.75 \mathrm{~cm}^{2}\) to lift the chair?

An underwater camera weighing \(1250 \mathrm{~N}\) in air is submerged and supported by a tether line. If the volume of the camera is \(8.30 \times 10^{-2} \mathrm{~m}^{3}\), what is the tension in the line?