Q: A steel anchor (density $$\rho_{steel} = 7800\ \mathrm{kg/m^3$}) $$with a volume of $$0.02\ \mathrm{m^3$} is $$fully submerged in seawater (density $$\rho_{water} = 1025\ \mathrm{kg/m^3$}). $$What is the magnitude of the buoyant force acting on the anchor?

$$F_b = 0.02 \times 1025 \times 9.8 = 200.9\ \mathrm{N}$$

Q: A hydraulic lift has a small piston with area $$A_1 = 0.01$$\ \mathrm{$$m^2$$}$$ and a large piston with area A_2$ = 0.5\ \mathrm{m^2$}. If a $$force of $$F_1 = 200$$\ \mathrm{N}$$ is applied to the small piston, what is the maximum weight that can be lifted by the large piston (neglecting the height difference)?

$$F_2$$ = $$F_1$$ \frac{$$A_2$$}{$$A_1$$} = 200 \times \frac{0.5}{0.01} = 10,000\ \mathrm{N}$$

Q: A diver descends to a depth of $$30\ \mathrm{m} in $$freshwater ($$\rho = 1000\ \mathrm{kg/m^3$}). $$What is the absolute pressure at this depth? (Assume atmospheric pressure $$p_0 = 1.01$$ \times $$10^5$$\ \mathrm{Pa}$$, g = 9.8$$\ \mathrm{$$m/s^2$$}$$)

$$p = p_0$ + \rho g h = 1.01 \times 10^5$ + 1000 \times 9.8 \times 30 = 3.95 \times 10^5$\ \mathrm{Pa}$$

Q: A car tire is inflated to a gauge pressure of $$2.2 \times 10^5$\ \mathrm{Pa}. $$What is the absolute pressure inside the tire if atmospheric pressure is $$1.01 \times 10^5$\ \mathrm{Pa}$$?

$$p_{abs} = p_{atm} + p_{gauge} = 1.01 \times 10^5$ + 2.2 \times 10^5$ = 3.21 \times 10^5$\ \mathrm{Pa}$$

Q: A Venturi meter is used to measure the flow speed of water in a pipe. At the narrowest part of the pipe, the cross-sectional area is halved compared to the wider section. If the speed in the wide section is $$2\ \mathrm{m/s}$$, what is the speed in the narrow section (assuming incompressible flow)?

$$v_2$$ = $$v_1$$ \frac{$$A_1$$}{$$A_2$$} = 2 \times \frac{1}{0.5} = 4\ \mathrm{m/s}$$

Q: A patient’s blood pressure is measured as $$120/80 mm Hg. $$What is the gauge pressure corresponding to the systolic value in pascals? ($$1\ \mathrm{mm\ Hg} = 133\ \mathrm{Pa})$$

$$120 \times 133 = 15,960\ \mathrm{Pa}$$

Q: A submarine hatch has an area of $$0.72\ \mathrm{m^2$}$$ and is located $$10\ \mathrm{m}$$ below the ocean surface ($$\rho_{water} = 1025\ \mathrm{kg/m^3$}$$, $$g = 9.8\ \mathrm{m/s^2$}). $$What is the force due to water pressure on the hatch (ignore atmospheric pressure inside the submarine)?

$$F = \rho g h A = 1025 \times 9.8 \times 10 \times 0.72 = 72,180\ \mathrm{N}$$

Question 1

A steel anchor (density $$\rho_{steel} = 7800\ \mathrm{kg/m^3$}) $$with a volume of $$0.02\ \mathrm{m^3$} is $$fully submerged in seawater (density $$\rho_{water} = 1025\ \mathrm{kg/m^3$}). $$What is the magnitude of the buoyant force acting on the anchor?

Accepted Answer

$$F_b = 0.02 	imes 1025 	imes 9.8 = 200.9\ \mathrm{N}$$

Question 2

A hydraulic lift has a small piston with area $$A_1 = 0.01$$\ \mathrm{$$m^2$$}$$ and a large piston with area A_2$ = 0.5\ \mathrm{m^2$}. If a $$force of $$F_1 = 200$$\ \mathrm{N}$$ is applied to the small piston, what is the maximum weight that can be lifted by the large piston (neglecting the height difference)?

Accepted Answer

$$F_2$$ = $$F_1$$ \frac{$$A_2$$}{$$A_1$$} = 200 	imes \frac{0.5}{0.01} = 10,000\ \mathrm{N}$$

Question 3

A diver descends to a depth of $$30\ \mathrm{m} in $$freshwater ($$ho = 1000\ \mathrm{kg/m^3$}). $$What is the absolute pressure at this depth? (Assume atmospheric pressure $$p_0 = 1.01$$ 	imes $$10^5$$\ \mathrm{Pa}$$, g = 9.8$$\ \mathrm{$$m/s^2$$}$$)

Accepted Answer

$$p = p_0$ + ho g h = 1.01 	imes 10^5$ + 1000 	imes 9.8 	imes 30 = 3.95 	imes 10^5$\ \mathrm{Pa}$$

Question 4

A block of wood (density $$600\ \mathrm{kg/m^3$}) $$floats in water. What fraction of the block's volume is submerged?

Accepted Answer

$$\frac{V_{sub}}{V_{total}} = \frac{\rho_{wood}}{\rho_{water}} = \frac{600}{1000} = 0.6$$

Question 5

A car tire is inflated to a gauge pressure of $$2.2 	imes 10^5$\ \mathrm{Pa}. $$What is the absolute pressure inside the tire if atmospheric pressure is $$1.01 	imes 10^5$\ \mathrm{Pa}$$?

Accepted Answer

$$p_{abs} = p_{atm} + p_{gauge} = 1.01 	imes 10^5$ + 2.2 	imes 10^5$ = 3.21 	imes 10^5$\ \mathrm{Pa}$$

Question 6

A Venturi meter is used to measure the flow speed of water in a pipe. At the narrowest part of the pipe, the cross-sectional area is halved compared to the wider section. If the speed in the wide section is $$2\ \mathrm{m/s}$$, what is the speed in the narrow section (assuming incompressible flow)?

Accepted Answer

$$v_2$$ = $$v_1$$ \frac{$$A_1$$}{$$A_2$$} = 2 	imes \frac{1}{0.5} = 4\ \mathrm{m/s}$$

Question 7

A patient’s blood pressure is measured as $$120/80 mm Hg. $$What is the gauge pressure corresponding to the systolic value in pascals? ($$1\ \mathrm{mm\ Hg} = 133\ \mathrm{Pa})$$

Accepted Answer

$$120 	imes 133 = 15,960\ \mathrm{Pa}$$

Question 8

A submarine hatch has an area of $$0.72\ \mathrm{m^2$}$$ and is located $$10\ \mathrm{m}$$ below the ocean surface ($$\rho_{water} = 1025\ \mathrm{kg/m^3$}$$, $$g = 9.8\ \mathrm{m/s^2$}). $$What is the force due to water pressure on the hatch (ignore atmospheric pressure inside the submarine)?

Accepted Answer

$$F = ho g h A = 1025 	imes 9.8 	imes 10 	imes 0.72 = 72,180\ \mathrm{N}$$

Question 9

Which of the following best explains why a steel ship floats on water, even though steel is denser than water?

Accepted Answer

The average density of the ship (including the air inside) is less than the density of water.

Question 10

A helium balloon (density $$0.179\ \mathrm{kg/m^3$}) is $$used to lift a payload of $$180\ \mathrm{kg} ($$including the balloon). If the density of air is $$1.29\ \mathrm{kg/m^3$}$$, what is the minimum volume of helium required? (Neglect the mass of the balloon material.)

Accepted Answer

$$V = \frac{180}{1.29 - 0.179} = 157\ \mathrm{m^3$}$$

Question 11

Which statement about pressure in a fluid at rest is correct?

Accepted Answer

Pressure at a given depth is the same in all directions.

Question 12

A container of water has a hole in its side near the bottom. If the container is dropped in free fall, what happens to the water flow from the hole?

Accepted Answer

The flow stops altogether.

Question 13

Which of the following is a consequence of Pascal’s Law?

Accepted Answer

A small force applied to a small piston can be transformed into a large force on a large piston in a hydraulic lift.

Question 14

According to Bernoulli’s equation, what happens to the pressure of a fluid as its speed increases in a horizontal pipe?

Accepted Answer

The pressure decreases.

Question 15

Which of the following best describes the difference between laminar and turbulent flow?

Accepted Answer

Laminar flow is smooth and orderly, while turbulent flow is chaotic and irregular.

Question 16

A nurse measures a patient’s blood pressure at the ankle, which is $$0.5\ \mathrm{m}$$ below the heart. If the density of blood is $$1060\ \mathrm{kg/m^3$}$$ and $$g = 9.8\ \mathrm{m/s^2$}$$, what is the increase in pressure compared to the heart?

Accepted Answer

$$\Delta p = ho g h = 1060 	imes 9.8 	imes 0.5 = 5,190\ \mathrm{Pa}$$

Question 17

Which of the following is true about surface tension?

Accepted Answer

It is caused by cohesive forces between molecules at the surface of a liquid.

Question 18

A pipe carries water from a reservoir at height $$h_1 to a $$lower point at height $$h_2. If $$the speed at the top is negligible, what is the speed at the lower point according to Bernoulli’s equation?

Accepted Answer

$$v_2$$ = \sqrt{2g($$h_1$$ - $$h_2$$)}$$

Chapter 12: Fluid Mechanics – Study Notes

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