Q: A barometer uses mercury to measure atmospheric pressure. If $$\rho_{Hg} = 1.3595 \times 10^4$ \ \text{kg/m}^3$$ and $$P_{atm} = 1.013 \times 10^5$ \ \text{Pa}$$, what is the height $$h of $$the mercury column?

$$h = \frac{P_{atm}}{\rho_{Hg} g} = \frac{1.013 \times 10^5$}{1.3595 \times 10^4$ \times 9.81} \approx 0.76 \ \text{m}$$

Q: A person weighs $$720 \ \text{N} in $$air and $$34.3 \ \text{N}$$ when fully submerged in water. What is the volume of the person?

$$V = \frac{720 - 34.3}{1000 \times 9.81} \approx 0.07 \ \text{m}^3$$

Question 1

A bird is able to walk on lily pads without sinking. Which physical principle best explains why the bird's large toes help it stay afloat?

Accepted Answer

The bird's toes increase the area, reducing the pressure exerted on the lily pad according to $$P = \frac{F}{A}.$$

Question 2

Given atmospheric pressure $$P_{atm} = 1.01 	imes 10^5$ \ 	ext{N/m}^2$$, what is the force exerted by the atmosphere on a hand with dimensions $$0.077 \ 	ext{m} 	imes 0.094 \ 	ext{m}$$?

Accepted Answer

$$F = 730 \ 	ext{N}$$

Question 3

A tire has a gauge pressure of $$35 \ 	ext{psi}$$ ($$241 \ 	ext{kPa}). $$What is the actual pressure inside the tire?

Accepted Answer

$$P = 342 \ 	ext{kPa}$$

Question 4

If you push down on a basketball with a force $$F = 22 \ 	ext{N}$$ over a circular area of diameter $$2.0 \ 	ext{cm}$$, what is the pressure applied?

Accepted Answer

$$P = \frac{F}{A} = \frac{22}{\pi (0.01)^2$} \approx 70,000 \ 	ext{Pa}$$

Question 5

What is the pressure at the bottom of a fluid column of height $$h$$ and density $$\rho$$, open to atmospheric pressure $$P_{atm}$$?

Accepted Answer

$$P_{bottom} = P_{atm} + \rho g h$$

Question 6

A swimmer releases a bubble underwater. As the bubble rises, what happens to its diameter?

Accepted Answer

The diameter increases because the pressure decreases as the bubble rises.

Question 7

A barometer uses mercury to measure atmospheric pressure. If $$ho_{Hg} = 1.3595 	imes 10^4$ \ 	ext{kg/m}^3$$ and $$P_{atm} = 1.013 	imes 10^5$ \ 	ext{Pa}$$, what is the height $$h of $$the mercury column?

Accepted Answer

$$h = \frac{P_{atm}}{ho_{Hg} g} = \frac{1.013 	imes 10^5$}{1.3595 	imes 10^4$ 	imes 9.81} \approx 0.76 \ 	ext{m}$$

Question 8

In a hydraulic lift, if the area of the large piston $$A_2 is 10 $$times the area of the small piston $$A_1$$, what is the relationship between the forces $$F_2$$ and $$F_1$$?

Accepted Answer

$$F_2 = 10$$ $$F_1$$

Question 9

A person weighs $$720 \ 	ext{N} in $$air and $$34.3 \ 	ext{N}$$ when fully submerged in water. What is the volume of the person?

Accepted Answer

$$V = \frac{720 - 34.3}{1000 	imes 9.81} \approx 0.07 \ 	ext{m}^3$$

Question 10

A clay bowl floats on water, but a clay sphere of the same mass sinks. Why does the bowl float?

Accepted Answer

The bowl's shape allows it to displace enough water to equal its weight, satisfying Archimedes' principle.

Question 11

A ship has two maximum load lines: one for freshwater and one for saltwater. Which line should be used for saltwater?

Accepted Answer

The bottom line, because saltwater is denser and the ship floats higher.

Question 12

A floating ice cube in a cup of water melts. What happens to the water level?

Accepted Answer

The water level remains the same.

Question 13

Water flows through a pipe with area $$A_1$$ and speed $$v_1. $$The pipe narrows to area $$A_2$$ and speed $$v_2. $$For an incompressible fluid, what is the continuity equation?

Accepted Answer

$$A_1$$ $$v_1$$ = $$A_2$$ $$v_2$$

Question 14

According to Bernoulli's equation, what happens to the pressure in a fluid as its speed increases?

Accepted Answer

Pressure decreases as speed increases.

Question 15

During a hurricane, a 42.6 m/s wind blows across a flat roof. What is the pressure difference between the air inside and above the roof? (Density of air $$= 1.29 \ 	ext{kg/m}^3)$$

Accepted Answer

$$\Delta P = \frac{1}{2} ho v^2$ = \frac{1}{2} 	imes 1.29 	imes (42.6)^2$ \approx 1,170 \ 	ext{Pa}$$

Question 16

A gardener wants water to exit from a tank at a depth $$h$$ below the surface. What is the speed of the water as it emerges?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 17

If the radius of an artery decreases by 20%, how does the required pressure difference to maintain the same volume flow rate change?

Accepted Answer

It increases by a factor of $$\left(\frac{1}{0.5}\$$right)^4$$ = 16$$

Question 18

Why do small drops of dew tend to be spherical?

Accepted Answer

Surface tension minimizes the surface area for a given volume, forming a sphere.

Chapter 15: Fluids – Structured Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards