Q: Which equation best describes the relationship between pressure, speed, and height in an ideal fluid along a streamline?

$$p + \frac{1}{2}\rho v^2$ + \rho g y = \text{constant}$$

Question 1

A barometer is used to measure atmospheric pressure. If water were used instead of mercury, what would be the approximate height of the water column required to measure standard atmospheric pressure? (Assume $$p_{atm} = 1.01 	imes 10^5$ Pa, $$ho_{water} = 1000$$ kg/m^3$, g = 9.8$ m/s^2$)

Accepted Answer

$$h \approx 10 m$$

Question 2

A patient raises her arm so that the blood pressure cuff is 15 cm above her heart. If the density of blood is $$1050 kg/m$^3$$, what is the error introduced in the pressure measurement? ($$g = 9.8 m/s$^2)$$

Accepted Answer

$$\Delta p = 1540 Pa$$

Question 3

According to Archimedes’ principle, what is the buoyant force on a 2.0 L block fully submerged in water? ($$\rho_{water} = 1000 kg/m$^3$$, $$g = 9.8 m/s$^2)$$

Accepted Answer

$$F_B = 19.6 N$$

Question 4

A horizontal pipe carries water from a wide section to a narrow section. If the speed of water in the wide section is $$2 m/s $$and the cross-sectional area is $$0.05 m$^2$$, what is the speed in the narrow section with area $$0.01 m$^2$$?

Accepted Answer

$$v_2 = 10$ m/s

Question 5

Which of the following best explains why airplanes can fly, according to the Bernoulli effect?

Accepted Answer

The pressure below the wing is higher than above, creating lift.

Question 6

A cylindrical pipe of radius $$r$$ and length $$L$$ carries a viscous fluid. If the radius is doubled, by what factor does the flow rate increase according to Poiseuille’s equation?

Accepted Answer

It increases by a factor of 16

Question 7

Blood flows through a vessel with a pressure drop of $$\Delta p$$, length $$L$$, and radius $$R. $$According to Poiseuille’s equation, which change will most effectively increase the flow rate?

Accepted Answer

Double the radius $$R$$

Question 8

A mass oscillates on a spring with period $$T = 2.0 s. $$How long does it take to go from the rightmost point to the leftmost point of its motion?

Accepted Answer

$$4.0 s$$

Question 9

Which of the following statements about simple harmonic motion (SHM) is correct?

Accepted Answer

The frequency depends on the mass and spring constant.

Question 10

A pendulum of length $$L$$ undergoes small oscillations. What is the restoring force acting on the mass for small angles $$	heta$$?

Accepted Answer

$$F = -mg\sin	heta$$

Question 11

In the circulatory system, where does most of the pressure drop occur?

Accepted Answer

In the capillaries and arterioles

Question 12

Which of the following is true about the velocity profile of a viscous fluid flowing through a tube?

Accepted Answer

The fluid moves fastest at the center.

Question 13

A ball is dropped into a bowl and oscillates about the equilibrium position. What is the restoring force responsible for the oscillation?

Accepted Answer

Gravitational force component toward equilibrium

Question 14

Which equation best describes the relationship between pressure, speed, and height in an ideal fluid along a streamline?

Accepted Answer

$$p + \frac{1}{2}ho v^2$ + ho g y = 	ext{constant}$$

Question 15

A Venturi tube is used to measure fluid speed. If the pressure difference between two points is increased, what happens to the fluid speed at the narrow section?

Accepted Answer

It increases

Question 16

Which of the following is a real-world application of the Magnus effect?

Accepted Answer

A spinning soccer ball curving in flight

Question 17

If the viscosity of a fluid decreases with increasing temperature, what happens to the flow rate through a tube for a fixed pressure difference?

Accepted Answer

The flow rate increases

Question 18

A mass $$m$$ hangs from a vertical spring with spring constant $$k. $$What is the equilibrium extension $$\Delta L of $$the spring?

Accepted Answer

$$\Delta L = \frac{mg}{k}$$

Question 19

Which of the following best describes the equation of continuity for incompressible fluid flow?

Accepted Answer

$$v_1A_1 = v_2A_2$$

Fluid Dynamics, Viscosity, Poiseuille’s Equation, and Oscillations: Physics for Life Sciences I (Lecture 23 Study Notes)

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