Physics 18, Fall 2008 Worksheet 18 Fluids I. Fluid Statics

Physics 18, Fall 2008 Worksheet 18 Fluids I. Fluid Statics 1. We know intuitively that the pressure at the bottom of the sea is large, while the pressure at the top of a mountain is small. Why is this so?

2. Pascal’s principle says that if a fluid is in static equilibrium (not flowing), then the pressure at a given depth below the surface is constant, despite the shape of the container. For instance, if your bathtub is filled with water, the pressure 6 cm below the surface at the middle of the tub equals the pressure 6 cm below the surface near the back of the tub. How do we know this must be so?

3. Two identical buckets are filled to the rim with water, but one has a block of wood floating in the water (and therefore contains a little less water). Which bucket, if either, is heavier?

4. A barge filled with scrap iron is in a canal lock. If the iron is thrown overboard, what happens to the water level in the lock? Explain.

5. A hollow spherical iron shell floats almost completely submerged in water. The outer diameter of the shell is 58.7 cm, and the density of iron is 7.87 g/cm3. Find the inner diameter of the shell. [Ans: 56.1 cm]

6. A spherical balloon is filled with helium, with a density of 0.18 kg/m3. The density of air is 1.3 kg/m3. What must the radius of the balloon be in order to lift a person weighing 75 kg, if the mass of the balloon (not including the helium) is 25 kg? [Ans: 2.8 m]

M,ρhelium R ρair

m

Adapted from: UCMerced Physics Discussion Worksheets

(Neglect the air displaced by the person.)

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Physics 18, Fall 2008

WS13

II. Fluid Dynamics B A 7. The particles shown are moving to the right through a tube with a steady flow. (a) How does the speed of the particles at A compare to the speed of the particles at B? Explain. (b) How does the pressure at A compare to the pressure at B? Explain.

8. The particles shown are moving to the right through a tube with a steady flow. (c) How does the speed of the particles at A compare to the speed of the particles at B? Explain. (d) How does the pressure at A compare to the pressure at B? Explain.

A

B

9. Smoke rises in a chimney faster when a breeze is blowing. Why? Why doesn't the smoke pour into the room containing the fireplace?

10. If you dangle two pieces of paper vertically, a few inches apart, and blow between them, how do you think they will move? Try it and see. Explain.

11. Two rowboats moving parallel to one another in the same direction are pulled toward one another. Two automobiles (or an automobile and a truck) moving parallel to one another in the same direction are also pulled together. Explain. 12. (a) Why does a stream of water from a faucet become narrower as it falls? (b) A stream of water shot straight up in a fountain breaks apart at the top. Why?

13. Water flows out of a hole in the side of a large tank at a distance h below the water surface as shown. The tank is open at the top. a. Show that the speed of the water emerging from the hole is v2 = 2gh. b. If the water were aimed straight upward coming out of the hole, to what height would it rise? Adapted from: UCMerced Physics Discussion Worksheets

h v

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Physics 18, Fall 2008

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14. When water drains out of a hole in the bottom of a tank, the stream radius contracts as the speed of the water increases. Assume that the stream starts with zero water velocity at the top of the tank, at a height H above the hole, and ignore all instabilities that will lead to breakup of the stream (turbulence, etc.). Find the distance d beneath the hole at which the radius of the stream is 80% of the hole radius. [Ans: 1.44 H] B

15. [Resnick, Halliday, & Krane, Ch. 18, Problem 21] A siphon is a device for removing liquid from a container that is h1 not to be tipped. It operates as shown. The tube must be initially filled, but once this has been done the liquid will flow until its level drops below the tube d A opening at A. The liquid has density ρ and negligible viscosity. h2 (e) With what speed does the liquid emerge from the tube at C? C (f) What is the pressure in the liquid at the topmost point B? (g) What is the greatest possible height h1 to which a siphon can lift water? [Hint: The pressure at the top cannot be less than zero.]

Adapted from: UCMerced Physics Discussion Worksheets

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