Question 1

A river's flow rate increases when the velocity of the water increases. Which equation best describes the relationship between flow rate ($$Q$$), cross-sectional area ($$A$$), and velocity ($$v) of $$the river?

Accepted Answer

$$Q = A v$$

Question 2

Water flows through a pipe with a cross-sectional area of $$0.05\ \mathrm{m}^2 at a $$velocity of $$3\ \mathrm{m/s}. $$What is the flow rate?

Accepted Answer

$$Q = 0.15\ \mathrm{m}^3/\mathrm{s}$$

Question 3

A garden hose with a radius of $$0.900\ \mathrm{cm} is $$attached to a nozzle with a radius of $$0.250\ \mathrm{cm}. If $$the flow rate is $$500\ \mathrm{cm}^3/\mathrm{s}$$, what is the speed of water in the nozzle?

Accepted Answer

$$v = 25.5\ \mathrm{cm/s}$$

Question 4

According to the equation of continuity, if the diameter of a pipe decreases, what happens to the velocity of an incompressible fluid flowing through it?

Accepted Answer

The velocity increases.

Question 5

Which equation represents the equation of continuity for an incompressible fluid?

Accepted Answer

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

Question 6

A fire hose with a diameter of $$9.8\ \mathrm{cm}$$ carries water at $$1.5\ \mathrm{m/s}. If $$the nozzle diameter is $$2.6\ \mathrm{cm}$$, what is the speed of water as it exits the nozzle?

Accepted Answer

$$v_2 = 21.2$$\ \mathrm{m/s}$$

Question 7

If the speed of a fluid increases as it flows through a constriction, what happens to the pressure according to Bernoulli's principle?

Accepted Answer

The pressure decreases.

Question 8

Which of the following is the correct form of Bernoulli's equation for a fluid flowing from point 1 to point 2?

Accepted Answer

$$p_1$$ + \frac{1}{2} \rho $$v_1^2$$ + \rho g $$y_1$$ = $$p_2$$ + \frac{1}{2} \rho $$v_2^2$$ + \rho g $$y_2$$

Question 9

A sump pump is draining a basement at $$Q = 0.00075\ \mathrm{m}^3/\mathrm{s}$$ with an output pressure of $$3.005\ \mathrm{N/m}^2. $$The water rises $$2.50\ \mathrm{m}$$ above the pump. What is the pressure at this point? (Assume $$\rho = 1000\ \mathrm{kg/m}^3$$, $$g = 9.8\ \mathrm{m/s}^2)$$

Accepted Answer

$$p = -24,497\ \mathrm{N/m}^2$$

Question 10

Which of the following best describes viscosity?

Accepted Answer

A measure of a fluid's resistance to flow.

Question 11

In a pipe carrying a viscous fluid, where is the velocity of the fluid the greatest?

Accepted Answer

At the center of the pipe.

Question 12

Which of the following statements about surface tension is correct?

Accepted Answer

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

Question 13

A pipe carries water from a lower elevation to a higher elevation. If the velocity remains constant, how does the pressure at the higher elevation compare to the lower elevation?

Accepted Answer

The pressure is lower at the higher elevation.

Question 14

Which real-world scenario best illustrates the Bernoulli effect?

Accepted Answer

An airplane wing generating lift due to faster airflow above the wing.

Question 15

If the flow rate through a pipe is constant and the pipe narrows, what must happen to the velocity of the fluid?

Accepted Answer

The velocity increases.

Question 16

Which of the following is NOT an assumption of Bernoulli's equation?

Accepted Answer

The fluid is compressible.

Question 17

A fluid flows through a horizontal pipe that narrows from $$A_1 to$$ $$A_2. If$$ $$A_2$$ \u003c $$A_1$$, which of the following is true about the pressure at $$A_2$$ compared to $$A_1$$?

Accepted Answer

The pressure at $$A_2 is $$less than at $$A_1.$$

Question 18

Which equation would you use to calculate the pressure difference between two points in a vertical pipe with stationary fluid?

Accepted Answer

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

Fluid Dynamics: Flow Rate, Continuity, Bernoulli’s Principle, Viscosity, and Surface Tension

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