Fluids Problems

Density and Pressure

1.  One of the concrete pillars that support a house is 2.2m tall and has a radius of 0.50m. The density of concrete is about 2.2x103 kg/m3. Find the weight of this pillar in pounds (1N = 0.2248lbs)

2.  An airtight box has a removable lid of area 1.3X10-2m2 and negligible weight. The box is taken up a mountain where the air pressure outside the box is 0.85x105Pa. The inside of the box is completely evacuated. What is the magnitude of the force required to pull the lid off the box?

3.  A glass bottle of soda is sealed with a screw cap. The absolute pressure of the carbon dioxide inside the bottle is 1.80x105Pa. Assuming that the top and bottom surfaces of the cap each have an area of 4.10x10-4m2, obtain the magnitude of the force that the screw thread exerts on the cap in order to keep in on the bottle. The air pressure outside the bottle is one atmosphere.

4.  A suitcase (mass m=16kg) is resting on the floor of an elevator. The part of the suitcase in contact with the floor measures 0.50m by 0.15m. The elevator is moving upward, the magnitude of its acceleration being 1.5m/s2. What pressure (in excess of atmospheric pressure) is applied to the floor beneath the suitcase?

5.  The main water line enters a house on the first floor. The line has a gauge pressure of 1.90X105 Pa.

a.  A faucet on the second floor, 6.50 above the first floor, is turned off. What is the gauge pressure at this faucet?

b.  How high could a faucet be before no water would flow from it, even if the faucet were open?

6.  Some researchers believe that the dinosaur Barosaurus held its head erect on a long neck, much as a giraffe does. If so, fossil remains indicate that its heart would have been about 12m below its brain. Assume that the blood has the density of water, and calculate the amount by which the blood pressure in the heart would have exceeded that in the brain. Size estimates for the single heart needed to withstand such a pressure range up to two tons. Alternately, Barosaurus may have had a number of smaller hearts.

7.  The human lungs can function satisfactorily up to a limit where the pressure difference between the outside and inside of the lungs is one-twentieth of an atmosphere. If a diver uses a snorkel for breathing, how far below the water can she swim? Assume the diver is in salt water whose density is 1025kg/m3.

Pascal’s Principle

8.  In the process of changing a flat tire, a motorist uses a hydraulic jack. She begins by applying a force of 45N to the input piston, which has a radius r1. As a result, the output plunger, which has a radius r2, applies a force to the car. The ratio r2/r1 has a value of 8.3. Ignore the height difference between the input piston and output plunger and determine the force that the output plunger applies to the car.

9.  The hydraulic oil in a car lift has a density of 8.3X102kg/m3. The weight of the input piston is negligible. The radii of the input piston and the out plunger are 7.70X10-3 and 0.125m, respectively. What input force F is needed to support the 24,500N combined weight of a car and the output plunger, (a) when the bottom surfaces of the piston and plunger are at the same level, and (b) the bottom surface of the output plunger is 1.30 m above that of the input piston.

Archimedes’ Principle

10.  A duck is floating on a lake with 25% of its volume beneath the water. What is the average density of the duck?

11.  The density of ice is 917 kg/m3, and the density of sea-water is 1025kg/m3. A swimming polar bear climbs onto a piece of floating ice that has a volume of 5.2m3. What is the weight of the heaviest bear that the ice can support without sinking completely beneath the water?

12.  An object is solid throughout. When the object is completely submerged in ethyl alcohol, its apparent weight is 15.2 N. When completely submerged in water, its apparent weight is 13.7N. What is the volume of the object? (Hint: the density of ethyl alcohol is 806kg/m3)

Equation of Continuity

13.  Oil is flowing with a speed of 1.22m/s through a pipeline with a radius of 0.305m. How many gallons of oil (1gal=3.79X10-3m3) flow in one day?

14.  A patient recovering from surgery is being given liquid intravenously. The fluid has a density of 1030 kg/m3, and 9.5 X 10-4 m3 of it flows into the patient every six hours. Find the mass flow rate in kg/s.

15.  The aorta carries blood away from the heart at a speed of about 40cm/s and has a radius of approximately 1.1cm. The aorta branches eventually into a large number of tiny capillaries that distribute the blood to the various body organs. In a capillary, the blood speed is approximately 0.07 cm/s, and the radius is about 6X10-4cm. Treat the blood as an incompressible fluid, and use these data to determine the approximate number of capillaries in the human body.

Bernoulli’s Equation

16.  Suppose that a 15m/s wind is blowing across the roof of your house. The density of air is 1.29kg/m3.

  1. Determine the reduction in pressure (below atmospheric pressure of stationary air) that accompanies the wind.
  2. Explain why some roofs are blown outward during high winds.

17.  An airplane wing is designed so that the speed of the air across the top of the wing is 251m/s when the speed of the air below the wing is 225m/s. The density of the air is 1.29kg/m3. What is the lifting force on a wing of area 24.0m2?

18.  Water is circulating through a close system of pipes in a two-floor apartment. On the first floor, the water has a gauge pressure of 3.4X105Pa and a speed of 2.1m/s. However, on the second floor, which is 4.0m higher, the speed of the water is 3.7m/s. The speeds are different because the pipe diameters are different. What is the gauge pressure of the water on the second floor?

19.  A small crack occurs in the base of a 15m high dam. The effective crack area through which water leaves is 1.30X10-3m2.

  1. Ignoring viscous losses, what is the speed of water flowing through the crack?
  2. How many cubic meters of water per second leave the dam?

20.  A fountain sends a stream of water straight up into the air to a maximum height of 5.00m. The effective cross-sectional area of the pipe feeding the fountain is 5.00X10-4m2. Neglecting air resistance and any viscous effects, determine how many gallons per minute are being used by the fountain. (Note: 1 gal = 3.79X10-3m3)