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Fluids, Buoyancy, Archimedes Principle


As a cargo ship is being loaded, it sinks deeper into the water. As the ship sinks deeper, its bouyancy
a. increases.
b. decreases.
c. stays the same.
d. can not be determined without more information.


a. Bouancy increases as more water is displaced.

Fluids, Buoyancy, Archimedes Problems

(See bottom of page for answers.)

1. Calculate the pressure created by ocean water (density = 1.025 g/cm3), at a depth of 11.0 Km.

2. Oil having a Reynold's number of 2500, specific gravity of 0.86, and viscosity at 20 degrees Celsius of 084 poise flows through a 5 inch diameter pipe.
a. What is the maximum average speed of the oil without turbulence?
b. How would the average speed change if the temperature of the oil was to rise?

3. The pressure in a tightly closed building is the same as outside, 988 mbars. The windows in this building are 1.2 m by 2.15 m. If a 23 m/s gust suddenly blows across the face of this building

a. What pressure difference across these windows does the wind create?

b. What force acts on each window?

4. A tennis ball has a density of 0.084 g/cc and a diameter of 3.8 cm. What force is required to submerge the ball in water?

5. Describe the relationship between fluid flow through a hole in a tank and the area of the hole.

6. Water (62 lb per cubic foot) is flowing into a 1 ft diameter pipe entrance at 100 ft/sec and 200 lb per square foot. Neglecting friction, what is the velocity and pressure at the 2 ft diameter exit?

7. A hot-air balloon consists of a basket and a 2.18x103 m3 envelope having a combined weight of 2.45 kN. What should be the temperature of the air used to inflate the envelope to provide a net lift of 2.67 kN? The surrounding air is 20ºC, has a weight of 11.41 N/m3, has an average molecular mass of 0.028 kg/mole, and is at a pressure of 1.0 atm.

8. Air pressure is 1x105 N/m2, air density is 1.3 kg/m3. How fast must air be blown across the top of a straw rising 0.10 m above the water in a glass, to make the water rise half way up the straw?

9. At what depth will a submersible experience 10.0 N per square millimeter pressure?

10. What lift does Bernoulli's principle predict for a wing of area 78 m2 if the air passes over the top surface at 260 m/s and the bottom surface at 150 m/s?

11. A body floats in liquid A with 9/10th of its volume immersed, while it floats in liquid B with 3/5th of its volume immersed. Compare the densities of the liquids.

12. At what depth will a diver experience 4 atmospheres pressure?

13. A 10 cm radius water main connects a hilltop reservoir to houses in a valley. The supply line to each house is 1cm radius. If only one house has water running, the flow is 0.25 L/s. What is the velocity of the water in the main and in the supply pipe? Where is the pressure highest?

14. The average velocity of flow in a river is 1.1 m/s where it is 0.5 m deep and 5 m wide. (A) What is its flow rate? (B) Another part of the river it is 2 m wide and 1 m deep. What are the flow rate and the average velocity?

15. A thin hollow sphere of mass 0.500 kg and diameter 0.180 m is filled with alcohol (= 806 kg/m3). Find the acceleration of the sphere after it is released under water.

16. A helium balloon tied by light string to an armrest in a stationary train hovers in the still air. When the train accelerates forward, what does the balloon do?

17. An empty ship is moored to a loading dock then filled with Styrofoam blocks. Does the ship float higher in the water or sink deeper?

18. An air bubble has a diameter of 1.0 cm at a depth of 18.0 m. What will the bubble's diameter at the surface? The temperature change is negligible.

Answers to Fluids, Buoyancy, Archimedes Problems

Selected solutions are printed below.
For solutions to all the problems on this page click here.

1. Given the density of ocean water is uniform at 1.025 g/cm3 = 1025 kg/m3, the weight of water is 1.005 x 104 N/m3 .

The pressure of water at this depth (the weight per square meter) would be
(1.005 x 104 N/m3)(11.0 x 103 m) = 1.105 x 108 N/m2 = 1.105 x 105 kPa
(about 16000 psi)

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7. The lifting force required = 2.45 kN + 2.67 kN = 5120 N
weight of 2.18x103 m3 air at 20ºC = 11.41 N/m3 * 2.18x103 m3 = 24874 N

Archimedes' principle informs us of buoyancy:
Lifting force = [weight of 2.18x103 m3 air at 20ºC] - [weight of 2.18x103 m3 hot air]
Substituting calculated values,
5120 N = 24874 N - [weight of 2.18x103 m3 hot air]
weight of 2.18x103 m3 hot air = 19754 N

From the ideal gas law, PV is proportional to WT
Since P and V are constant,
W1T1 = W2T2
(W1 / W2)T1 = T2
(24874 N / 19754 N)(293 K) = 369 K
365 K = 96ºC

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