Q: Atmospheric pressure at sea level is defined as 1 atm. What is its value in pascals?

$$1 \text{atm} = 101,000 \text{Pa}$$

Q: A suction cup is used to suspend an object from a ceiling. If the air pressure is $$101,000 \text{Pa}$$ and the suction cup has a radius of $$0.05 \text{m}$$, what is the maximum mass that can be suspended? (Use $$g = 9.8 \text{m/s}^2)$$

$$m = \frac{p \pi r^2$}{g} = \frac{101,000 \times \pi \times (0.05)^2$}{9.8} \approx 81 \text{kg}$$

Q: A pressure gauge reads a value of $$35 \text{psi}. $$What is the absolute pressure in pascals, if atmospheric pressure is $$101,000 \text{Pa}$$? ($$1 \text{psi} = 6,890 \text{Pa})$$

$$p = p_g + p_{atm} = 35 \times 6,890 + 101,000 = 341,150 \text{Pa}$$

Q: A crown weighs $$8.30 \text{N} in $$air and $$7.81 \text{N}$$ underwater. If the density of water is $$1,000 \text{kg/m}^3$$, what is the density of the crown?

$$\rho_o = \frac{\rho_f w_o}{F_B} = \frac{1,000 \times 8.30}{0.49} = 17,000 \text{kg/m}^3$$

Q: A wooden block floats in water with $$5.8 \text{cm}$$ submerged and in an unknown liquid with $$4.6 \text{cm}$$ submerged. What is the density of the unknown liquid?

$$\rho_u = \frac{h_w}{h_u} \rho_w = \frac{5.8}{4.6} \times 1,000 = 1,300 \text{kg/m}^3$$

Question 1

Which statement best explains why gases are compressible while liquids are not, based on their molecular structure?

Accepted Answer

Gas molecules are far apart, allowing them to be compressed, while liquid molecules are close together, making liquids incompressible.

Question 2

A 1 m × 1 m × 1 m cube is subdivided into smaller cubes with sides of 1 cm. How many 1 cm³ cubes are in the larger cube?

Accepted Answer

1,000,000

Question 3

If water squirts out of holes at different depths in a container, which hole will produce the fastest stream and why?

Accepted Answer

The lowest hole, because pressure increases with depth according to $$p = p_0$ + \rho g d.$$

Question 4

What is the formula for pressure exerted by a fluid on a surface, and what are its SI units?

Accepted Answer

Pressure is given by $$p = \frac{F}{A}$$ and its SI unit is the pascal ($$1 	ext{Pa} = 1 	ext{N}/	ext{m}^2).$$

Question 5

In a weightless environment, which statement about pressure in fluids is correct?

Accepted Answer

Liquids do not exert forces on the walls, while gases exert pressure due to molecular collisions.

Question 6

Atmospheric pressure at sea level is defined as 1 atm. What is its value in pascals?

Accepted Answer

$$1 	ext{atm} = 101,000 	ext{Pa}$$

Question 7

A suction cup is used to suspend an object from a ceiling. If the air pressure is $$101,000 	ext{Pa}$$ and the suction cup has a radius of $$0.05 	ext{m}$$, what is the maximum mass that can be suspended? (Use $$g = 9.8 	ext{m/s}^2)$$

Accepted Answer

$$m = \frac{p \pi r^2$}{g} = \frac{101,000 	imes \pi 	imes (0.05)^2$}{9.8} \approx 81 	ext{kg}$$

Question 8

What is the hydrostatic pressure at depth $$d in a $$liquid of density $$\rho$$, with surface pressure $$p_0$$?

Accepted Answer

$$p = p_0$ + \rho g d$$

Question 9

In a connected liquid in hydrostatic equilibrium, what can be said about the pressure at points on the same horizontal line?

Accepted Answer

The pressure is the same at all points on a horizontal line.

Question 10

A pressure gauge reads a value of $$35 	ext{psi}. $$What is the absolute pressure in pascals, if atmospheric pressure is $$101,000 	ext{Pa}$$? ($$1 	ext{psi} = 6,890 	ext{Pa})$$

Accepted Answer

$$p = p_g + p_{atm} = 35 	imes 6,890 + 101,000 = 341,150 	ext{Pa}$$

Question 11

A barometer measures atmospheric pressure by the height $$h of a $$liquid column. Which equation relates atmospheric pressure to the height and density of the liquid?

Accepted Answer

$$p_{atm} = \rho g h$$

Question 12

According to Archimedes’ principle, what is the magnitude of the buoyant force $$F_B on an $$object immersed in a fluid?

Accepted Answer

$$F_B = \rho_f V_f g$$

Question 13

A crown weighs $$8.30 	ext{N} in $$air and $$7.81 	ext{N}$$ underwater. If the density of water is $$1,000 	ext{kg/m}^3$$, what is the density of the crown?

Accepted Answer

$$ho_o = \frac{ho_f w_o}{F_B} = \frac{1,000 	imes 8.30}{0.49} = 17,000 	ext{kg/m}^3$$

Question 14

A wooden block floats in water with $$5.8 	ext{cm}$$ submerged and in an unknown liquid with $$4.6 	ext{cm}$$ submerged. What is the density of the unknown liquid?

Accepted Answer

$$ho_u = \frac{h_w}{h_u} ho_w = \frac{5.8}{4.6} 	imes 1,000 = 1,300 	ext{kg/m}^3$$

Question 15

Which of the following best describes laminar flow in fluids?

Accepted Answer

Fluid velocity is constant and flows in parallel layers without mixing.

Question 16

The equation of continuity for incompressible fluids is $$v_1$$ $$A_1$$ = $$v_2$$ $$A_2. $$What does this imply about fluid speed in a pipe?

Accepted Answer

Fluid speed increases as the cross-sectional area decreases.

Question 17

Bernoulli’s equation for ideal fluids is $$p_1$$ + \frac{1}{2} \rho $$v_1^2$$ = $$p_2$$ + \frac{1}{2} \rho $$v_2^2$. What happens to pressure as fluid speed increases?

Accepted Answer

Pressure decreases as fluid speed increases.

Question 18

Poiseuille’s equation for viscous flow is $$Q = \frac{\pi R^4$}{8 \eta} \frac{\Delta p}{L}. If $$the radius of the tube is halved, what happens to the volume flow rate $$Q$$?

Accepted Answer

The flow rate decreases by a factor of 16.

Fluids: Properties, Pressure, and Dynamics

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