Q: Which equation correctly expresses how pressure increases with depth in a fluid?

$$p_{\text{bottom}} = p_{\text{top}} + \rho g d$$

Q: Absolute pressure in a fluid is given by which equation?

$$P_{\text{abs}} = P_{g} + P_{\text{atm}}$$

Q: A net force due to a pressure difference across a surface is given by which equation?

$$F_{\text{net}} = (p_2$ - p_1$)A$$

Q: What is the magnitude of the buoyant force on an object submerged in a fluid of density $$\rho_{\text{fluid}}$$, displacing a volume $$V_{\text{displaced}}$$? Use $$g$$ for gravity.

$$F_b = \rho_{\text{fluid}} V_{\text{displaced}} g$$

Question 1

Which of the following best describes the SI unit of density?

Accepted Answer

kg/m\^3

Question 2

A whole chicken has a mass of 2.3 kg and a radius of 8.0 cm. What is its approximate density in kg/m\^3? Use $$V = \frac{4\pi R^3$}{3}.$$

Accepted Answer

1070 kg/m\^3

Question 3

Which statement about pressure in fluids is correct?

Accepted Answer

Pressure in fluids is a scalar and acts perpendicular to surfaces.

Question 4

An elephant with a mass of 3000 kg stands on four feet, each with a diameter of 50 cm. What is the pressure exerted by one foot? Use $$p = \frac{F}{A}$$ and $$A = \pi r^2$.

Accepted Answer

3.8 	imes $$10^3$$ 	ext{ Pa}

Question 5

You are walking on a frozen lake and hear the ice cracking. What is the best strategy to get off the ice safely?

Accepted Answer

Lie down flat on the ice and crawl toward shore.

Question 6

Which equation correctly expresses how pressure increases with depth in a fluid?

Accepted Answer

$$p_{	ext{bottom}} = p_{	ext{top}} + ho g d$$

Question 7

A research submarine operates at a depth of 85.0 m below the ocean surface. If the hatch has an area of 2.00 m\^2, what force is required to push it open? Use $$p_{	ext{water}} = p_0$ + ho g d$$ and $$F = p_{	ext{water}} 	imes A. $$Assume $$p_0 = 1.01$$ 	imes $$10^5 N/m$$\^2$$, $$ho = 1.03 	imes $$10^3 kg/m$$\^3$$, g = 9.8$ m/s\^2$.

Accepted Answer

2.8 	imes $$10^5$$ 	ext{ N}

Question 8

Which of the following best defines gauge pressure?

Accepted Answer

The pressure measured relative to atmospheric pressure.

Question 9

Absolute pressure in a fluid is given by which equation?

Accepted Answer

$$P_{	ext{abs}} = P_{g} + P_{	ext{atm}}$$

Question 10

In an IV infusion, the gauge pressure inside the vein is 5980 Pa. The fluid has a density of 1050 kg/m\^3. What is the minimum height $$h of $$the reservoir above the arm for fluid to enter the vein? Use $$P = \rho g h$$ and $$g = 9.8 m/s$$\^2$.

Accepted Answer

0.581 m

Question 11

Three containers are filled with water to the same height and have the same base area, but different shapes and total weights of water. Which container has the greatest total force acting on its base?

Accepted Answer

All three are equal

Question 12

A net force due to a pressure difference across a surface is given by which equation?

Accepted Answer

$$F_{	ext{net}} = (p_2$ - p_1$)A$$

Question 13

Which of the following statements about buoyant force is correct?

Accepted Answer

The buoyant force is the net upward force on an object in a fluid.

Question 14

According to Archimedes’ Principle, the buoyant force on an object is equal to:

Accepted Answer

The weight of the fluid displaced by the object.

Question 15

What is the magnitude of the buoyant force on an object submerged in a fluid of density $$ho_{	ext{fluid}}$$, displacing a volume $$V_{	ext{displaced}}$$? Use $$g$$ for gravity.

Accepted Answer

$$F_b = ho_{	ext{fluid}} V_{	ext{displaced}} g$$

Question 16

A solid plastic ball of density $$6.00 	imes 10^2$ kg/m\^3 and radius 2.00 cm is attached by a string to the bottom of an aquarium filled with fresh water. What is the direction of the tension in the string?

Accepted Answer

Downward, opposing the net upward force.

Question 17

A piece of balsa wood with density 0.50 g/cm\^3 is released under water. What is its initial acceleration?

Accepted Answer

9.8 m/s\^2

Question 18

A boat floats in both fresh water and salt water. Where is the buoyant force greater on the boat?

Accepted Answer

The buoyant force is the same in both cases

Chapter 13: Fluid Mechanics – Density, Pressure, and Buoyancy

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