Q: A tank is open to the atmosphere and filled with water to a height $$h = 5\ \mathrm{m}. $$What is the absolute pressure at the bottom of the tank? ($$\rho_{water} = 1000\ \mathrm{kg/m^3$}$$, $$g = 9.8\ \mathrm{m/s^2$}$$, $$P_{atm} = 1.01 \times 10^5$\ \mathrm{Pa})$$

$$P = P_{atm} + \rho g h = 1.01 \times 10^5$ + 4.9 \times 10^4$ = 1.5 \times 10^5$\ \mathrm{Pa}$$

Q: Bernoulli's equation for a streamline in steady, incompressible flow is:

$$P + \frac{1}{2} \rho v^2$ + \rho g h = \text{constant}$$

Q: A pipe carries water from a reservoir at height $$h_1 = 10$$\ \mathrm{m}$$ to a lower point at h_2$ = 2\ \mathrm{m}. If $$the velocity at the top is negligible, what is the velocity at the lower point? ($$g = 9.8\ \mathrm{m/s^2$})$$

$$v_2$$ = \sqrt{2g($$h_1$$ - $$h_2$$)} = \sqrt{2 \times 9.8 \times 8} \approx 12.5\ \mathrm{m/s}$$

Question 1

Which of the following statements best describes the condition for a fluid to be considered incompressible in the context of fluid statics?

Accepted Answer

The fluid's density remains constant throughout its volume.

Question 2

A block of wood with a density of $$\rho_{wood} = 600\ \mathrm{kg/m^3$}$$ floats in water ($$\rho_{water} = 1000\ \mathrm{kg/m^3$}). $$What fraction of the block's volume is submerged?

Accepted Answer

$$0.6$$

Question 3

Which equation correctly relates pressure, force, and area in fluids?

Accepted Answer

$$P = \dfrac{F}{A}$$

Question 4

A diver descends to a depth of $$30\ \mathrm{m} in $$seawater ($$\rho = 1030\ \mathrm{kg/m^3$}). $$What is the gauge pressure at this depth? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$P = \rho g h = 303,540\ \mathrm{Pa}$$

Question 5

Which principle states that a pressure change in a confined, incompressible fluid is transmitted equally in all directions throughout the fluid?

Accepted Answer

Pascal's Principle

Question 6

A hydraulic lift has a small piston of area $$A_1 = 0.01$$\ \mathrm{$$m^2$$}$$ and a large piston of area A_2$ = 0.5\ \mathrm{m^2$}. If a $$force of $$F_1 = 200$$\ \mathrm{N}$$ is applied to the small piston, what is the force F_2$ exerted by the large piston?

Accepted Answer

$$F_2$$ = $$F_1$$ \dfrac{$$A_2$$}{$$A_1$$} = 10,000\ \mathrm{N}$$

Question 7

According to Archimedes' Principle, what is the buoyant force acting on a submerged object?

Accepted Answer

$$F_{buoyant} = \rho_{fluid} V_{displaced} g$$

Question 8

Water flows through a pipe with cross-sectional area $$A_1 = 0.02$$\ \mathrm{$$m^2$$}$$ at velocity v_1$ = 3\ \mathrm{m/s}. $$The pipe narrows to $$A_2 = 0.01$$\ \mathrm{$$m^2$$}$$. What is the velocity v_2$ in the narrow section?

Accepted Answer

$$v_2 = 6$$\ \mathrm{m/s}$$

Question 9

Which equation represents the continuity equation for incompressible fluid flow?

Accepted Answer

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

Question 10

A tank is open to the atmosphere and filled with water to a height $$h = 5\ \mathrm{m}. $$What is the absolute pressure at the bottom of the tank? ($$ho_{water} = 1000\ \mathrm{kg/m^3$}$$, $$g = 9.8\ \mathrm{m/s^2$}$$, $$P_{atm} = 1.01 	imes 10^5$\ \mathrm{Pa})$$

Accepted Answer

$$P = P_{atm} + ho g h = 1.01 	imes 10^5$ + 4.9 	imes 10^4$ = 1.5 	imes 10^5$\ \mathrm{Pa}$$

Question 11

Bernoulli's equation for a streamline in steady, incompressible flow is:

Accepted Answer

$$P + \frac{1}{2} ho v^2$ + ho g h = 	ext{constant}$$

Question 12

A pipe carries water from a reservoir at height $$h_1 = 10$$\ \mathrm{m}$$ to a lower point at h_2$ = 2\ \mathrm{m}. If $$the velocity at the top is negligible, what is the velocity at the lower point? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v_2$$ = \sqrt{2g($$h_1$$ - $$h_2$$)} = \sqrt{2 	imes 9.8 	imes 8} \approx 12.5\ \mathrm{m/s}$$

Question 13

Which of the following is NOT a common density value listed in the notes?

Accepted Answer

$$\rho_{gold} = 5000\ \mathrm{kg/m^3$}$$

Question 14

If the pressure at point 1 in a fluid is $$P_1$$ and at point 2 is $$P_2$$, and the vertical positions are $$y_1$$ and $$y_2$$, which equation correctly relates these quantities for a static fluid?

Accepted Answer

$$P_2$$ = $$P_1$$ - \rho g ($$y_2$$ - $$y_1$$)$$

Question 15

A syringe is used to inject fluid into a vein. If the plunger area is $$A_1 = 0.0005$$\ \mathrm{$$m^2$$}$$ and the force applied is F_1$ = 5\ \mathrm{N}$$, what is the pressure exerted by the plunger?

Accepted Answer

$$P = \dfrac{F_1$}{A_1$} = 10,000\ \mathrm{Pa}$$

Question 16

A water jet exits a pipe of radius $$r = 0.05\ \mathrm{m} at $$velocity $$v = 6\ \mathrm{m/s}. $$What is the volumetric flow rate $$Q$$?

Accepted Answer

$$Q = A v = \pi r^2$ v = \pi (0.05)^2$ 	imes 6 \approx 0.047\ \mathrm{m^3$/s}$$

Question 17

Which of the following best explains why atmospheric pressure decreases with altitude?

Accepted Answer

There is less air above a given point as altitude increases, so the weight of the air column decreases.

Question 18

A sealed container is filled with air at $$P = 1.5 	imes 10^5$\ \mathrm{Pa}. If $$the area of the lid is $$0.2\ \mathrm{m^2$}$$, what is the force exerted on the lid by the air?

Accepted Answer

$$F = P 	imes A = 3.0 	imes 10^4$\ \mathrm{N}$$

Fluid Mechanics: Density, Pressure, and Fluid Flow

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