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Chapter 10: Q14Q (page 260)

A tall Styrofoam cup is filled with water. Two holes are punched in the cup near the bottom, and water begins rushing out. If the cup is dropped so it falls freely, will the water continue to flow from the holes? Explain.

Short Answer

Expert verified

Due to the free fall of both water and the cup, the water will not flow from the holes.

Step by step solution

01

Understanding the free fall in the case of the Styrofoam cup

In the free fall, the gravity effect is considered to be the same. The Styrofoam cup and the water will experience the same acceleration due to gravity when both are falling.

02

Understanding the reason the water continues to flow from the holes or not

The water should have a higher acceleration than the gravity acceleration for the water flow to through the holes.

Because of the free-falling condition, both will fall together with the same velocity. The friction is negligible here.

The pressure drop is the difference between the water pressure on the bottom of the cup and atmospheric pressure. Since the lower molecules of the water did not hold the water molecules above the cup, therefore there will be no pressure difference between the bottom of the cup and the top.

Thus, the water will not continue to flow from the holes.

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Most popular questions from this chapter

(II) (a) Determine the total force and the absolute pressure on the bottom of a swimming pool 28.0 m by 8.5 m whose uniform depth is 1.8 m. (b) What will be the pressure against the side of the pool near the bottom?

A barge filled high with sand approaches a low bridge over the river and cannot quite pass under it. Should sand be added to, or removed from, the barge? [Hint: Consider Archimedes鈥� principle.]

Archimedes' principle can be used to determine the specific gravity of a solid using a known liquid(Example 10鈥�8). The reverse can be done as well. (a) Asan example, a 3.80-kg aluminum ball has an apparent mass of 2.10 kg when submerged in a particular liquid: calculate the density of the liquid. (b) Determine a formula for finding the density of a liquid using this procedure.

Two ships moving in parallel paths close to one another risk colliding. Why?

(a) Show that the flow speed measured by a venturi meter (see Fig. 10-29) is given by the relation

\({{\bf{v}}_{\bf{1}}}{\bf{ = }}{{\bf{A}}_{\bf{2}}}\sqrt {\frac{{{\bf{2}}\left( {{{\bf{P}}_{\bf{1}}}{\bf{ - }}{{\bf{P}}_{\bf{2}}}} \right)}}{{{\bf{\rho }}\left( {{\bf{A}}_{\bf{1}}^{\bf{2}}{\bf{ - A}}_{\bf{2}}^{\bf{2}}} \right)}}} \).

(b) A venturi meter is measuring the flow of water; it has a main diameter of \({\bf{3}}{\bf{.5\;cm}}\) tapering down to a throat diameter of \({\bf{1}}{\bf{.0\;cm}}\). If the pressure difference is measured to be \({\bf{18\;mm - Hg}}\), what is the speed of the water entering the venturi throat?
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