AP Physics 2: 1.6 Conservation of  Energy in Fluid Flow – Exam Style questions with Answer- MCQ

Question

An ideal fluid flows from left to right in the horizontal pipe shown in the figure. The fluid enters the left side of the pipe with speed v, where the diameter of the pipe is d. The pipe then narrows to a diameter of d/2.Does the pressure of the fluid change as the pipe becomes narrower, and why or why not?

A Yes, because the kinetic energy of the fluid changes but the total gravitational potential energy of the fluid-Earth system is constant.

B Yes, because there must be a compensation for the smaller surface area of the narrower pipe.

C No, because the atmospheric pressure at both ends of the pipe is constant.

D No, because both sections of the pipe are at the same height.

▶️Answer/Explanation

Ans:A

 Applying Bernoulli’s equation, \(P_1+ρgy_1+\frac{1}{2}ρv^2_1=P_2+ρgy_2+\frac{1}{2}ρv^2_2\) , the potential energy terms cancel because the height of the fluid does not change. So \(P_1+\frac{1}{2}ρv^2_1=P_2+\frac{1}{2}ρv^2_2\). If the speed changes as the pipe becomes narrower, then the pressure does also.

Question

The figure shows a horizontal pipe with sections with different cross-sectional areas. Small tubes extend from the top of each section. The cross-sectional area of the pipe at location C is half that at A, and the areas at A and D are the same. Water flows in the pipe from left to right. Which of the following correctly ranks the height h of the water in the tubes above the labeled locations?

A \(h_A=h_B=h_C=h_D\)

B \(h_A>h_B>h_C>h_D\)

C \((h_A=h_D)>h_B>h_C\)

D \(h_C>h_B>(h_A=h_D)\)

▶️Answer/Explanation

Ans:C

 According to Bernoulli’s equation, the pressure is less in a liquid that is moving faster. The speed of liquid is inversely proportional to the cross-sectional area it moves through. So the narrowest part of the pipe has the highest speed and the lowest pressure, and it will support the shortest column of water.

Question

Which of the following graphs best represents the absolute pressure \(P_{abs}\ at a point in a liquid near Earth’s surface as a function of the depth h

of the point below the surface of the liquid?

▶️Answer/Explanation

Ans:C

The relationship between \(P_{abs}\) and atmospheric pressure \(P_{atm}\) is \(P_{abs}=P_{atm}+ρgh\) . This is a linear relationship because ρ and g are constants, with a y-intercept equal to Patm.

Question

In the figure, water flows from a section of pipe with a smaller radius to a section of pipe with a larger radius. How do the pressure and velocity in the wider pipe compare to those in the narrower pipe?

 

▶️Answer/Explanation

Ans:B

 According to the equation of continuity, the velocity of the water in the wider pipe is less than in the narrower pipe. According to Bernoulli’s equation, when water does not change vertical position, a lesser velocity corresponds to a greater pressure.

Question

                     

The figure shows a container filled with water to a depth d. The container has a hole a distance y above its bottom, allowing water to exit with an initially horizontal velocity. Which of the following correctly predicts and explains how the speed of the water as it exits the hole would change if the distance y above the bottom of the container increased?

A The speed would decrease because the water pressure at the depth of the hole would decrease.

B The speed would decrease because the air pressure just outside of the hole would decrease.

C The speed would increase because more gravitational potential energy is being converted to kinetic energy

D The speed would increase because there is more water below the hole pushing up on the water near the hole.

▶️Answer/Explanation

Ans:A

The pressure increase in the container with depth is given by \(ρgΔh\) , where Δh is the distance below the surface of the water. According to Bernoulli’s equation, the square of the speed of the water is proportional to the water pressure \(ρgΔh\), which is decreasing because Δh decreases as y increases.

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