Q: A submarine is submerged 200 meters below the surface of the ocean. If the density of seawater is $$\rho = 1025\ \mathrm{kg/m^3$}$$ and atmospheric pressure at the surface is $$P_0 = 1.01$$ \times $$10^5$$\ \mathrm{Pa}$$, what is the absolute pressure on the submarine at this depth? (Take g = 9.8$$\ \mathrm{$$m/s^2$$}$$)

$$P = 2.11 \times 10^6$\ \mathrm{Pa}$$

Q: A block of wood floats in water with 60% of its volume submerged. What is the density of the wood if the density of water is $$1000\ \mathrm{kg/m^3$}$$?

$$\rho_{\text{wood}} = 600\ \mathrm{kg/m^3$}$$

Q: A nurse uses a syringe with a plunger area of $$2 \times 10$$^{-4}$$\ \mathrm{m^2$} to $$inject medicine. If she applies a force of $$4\ \mathrm{N}$$, what is the pressure exerted by the plunger?

$$P = 2 \times 10^4$\ \mathrm{Pa}$$

Question 1

A submarine is submerged 200 meters below the surface of the ocean. If the density of seawater is $$ho = 1025\ \mathrm{kg/m^3$}$$ and atmospheric pressure at the surface is $$P_0 = 1.01$$ 	imes $$10^5$$\ \mathrm{Pa}$$, what is the absolute pressure on the submarine at this depth? (Take g = 9.8$$\ \mathrm{$$m/s^2$$}$$)

Accepted Answer

$$P = 2.11 	imes 10^6$\ \mathrm{Pa}$$

Question 2

A hydraulic lift uses Pascal's Principle to lift a car. If the small piston has an area of $$0.01\ \mathrm{m^2$}$$ and the large piston has an area of $$0.5\ \mathrm{m^2$}$$, what force must be applied to the small piston to lift a $$10,000\ \mathrm{N}$$ car?

Accepted Answer

$$F = 200\ \mathrm{N}$$

Question 3

A block of wood floats in water with 60% of its volume submerged. What is the density of the wood if the density of water is $$1000\ \mathrm{kg/m^3$}$$?

Accepted Answer

$$ho_{	ext{wood}} = 600\ \mathrm{kg/m^3$}$$

Question 4

Water flows through a horizontal pipe that narrows from a cross-sectional area of $$0.05\ \mathrm{m^2$} to$$ $$0.01\ \mathrm{m^2$}. If $$the speed in the wider section is $$2\ \mathrm{m/s}$$, what is the speed in the narrower section?

Accepted Answer

$$v_2 = 10$$\ \mathrm{m/s}$$

Question 5

A tank is filled with water to a height of $$4\ \mathrm{m}. $$What is the speed of water exiting a small hole at the bottom of the tank according to Torricelli's Law? (Neglect air pressure and take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = 12.5\ \mathrm{m/s}$$

Question 6

A manometer is used to measure the pressure difference between two points in a pipe carrying oil ($$\rho = 850\ \mathrm{kg/m^3$}). If $$the height difference in the manometer is $$0.3\ \mathrm{m}$$, what is the pressure difference?

Accepted Answer

$$\Delta P = 2505\ \mathrm{Pa}$$

Question 7

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

Accepted Answer

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

Question 8

A soap bubble has a radius $$r. $$What is the excess pressure inside the bubble due to surface tension $$\gamma$$?

Accepted Answer

$$\Delta P = \dfrac{4\gamma}{r}$$

Question 9

A nurse uses a syringe with a plunger area of $$2 	imes 10$$^{-4}$$\ \mathrm{m^2$} to $$inject medicine. If she applies a force of $$4\ \mathrm{N}$$, what is the pressure exerted by the plunger?

Accepted Answer

$$P = 2 	imes 10^4$\ \mathrm{Pa}$$

Question 10

A horizontal pipe carries water at a speed of $$3\ \mathrm{m/s} in a $$section with a diameter of $$0.2\ \mathrm{m}. $$What is the volume flow rate $$Q$$?

Accepted Answer

$$Q = 0.094\ \mathrm{m^3$/s}$$

Question 11

Which of the following statements about Bernoulli's Equation is correct?

Accepted Answer

It expresses the conservation of energy for an incompressible, non-viscous fluid.

Question 12

A cube of side $$0.1\ \mathrm{m} is $$completely submerged in oil ($$\rho = 900\ \mathrm{kg/m^3$}). $$What is the magnitude of the buoyant force acting on the cube? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$F_B = 8.82\ \mathrm{N}$$

Question 13

Which of the following best explains why the pressure at the bottom of a swimming pool is greater than at the surface?

Accepted Answer

Pressure increases with depth due to the weight of the water above.

Question 14

A fluid flows through a pipe with varying diameter. If the velocity at point 1 is $$v_1$$ and the cross-sectional area is $$A_1$$, and at point 2 the area is $$A_2 = 2A_1$, what is the velocity v_2$ at point 2?

Accepted Answer

$$v_2$$ = \dfrac{$$v_1$$}{2}$$

Question 15

A glass capillary tube is dipped into water. Which property is primarily responsible for the water rising in the tube?

Accepted Answer

Surface tension

Question 16

A fluid has a viscosity coefficient $$\eta. $$According to the formula $$F = \eta \dfrac{vA}{L}$$, which change will decrease the viscous force $$F if $$all other variables are held constant?

Accepted Answer

Increasing the length $$L of $$the pipe

Question 17

Which of the following is NOT an assumption of the ideal fluid model used in Bernoulli's equation?

Accepted Answer

The fluid is compressible.

Question 18

A diver releases an air bubble at a depth of $$30\ \mathrm{m} in a $$lake. As the bubble rises to the surface, what happens to its volume?

Accepted Answer

The volume increases because the pressure decreases.

Question 19

A sealed tank contains oil ($$ho = 900\ \mathrm{kg/m^3$}) to a $$depth of $$5\ \mathrm{m}. If $$the air above the oil is at a gauge pressure of $$2 	imes 10^5$\ \mathrm{Pa}$$, what is the absolute pressure at the bottom of the tank? (Take $$g = 9.8\ \mathrm{m/s^2$}$$ and atmospheric pressure $$P_{atm} = 1.01 	imes 10^5$\ \mathrm{Pa})$$

Accepted Answer

$$P_{abs} = 3.44 	imes 10^5$\ \mathrm{Pa}$$

Question 20

A plastic ball with a volume of $$0.002\ \mathrm{m^3$} is $$held completely submerged in water. What is the buoyant force acting on the ball? (Take $$\rho_{water} = 1000\ \mathrm{kg/m^3$}$$, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$F_B = 19.6\ \mathrm{N}$$

Fluid Mechanics: Key Concepts and Formulas (AP Physics/College Physics Study Guide)

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