Physics quiz question: constant cross-section pipe flow

Physics 5A Quiz 5, Spring Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Problem 9.51

[Version 1]

[3.0 points.] Water flows through a pipe with a speed of 0.80 m/s through a pipe of 2.0 cm inside radius, at point [1]. The pipe has the same radius of 2.0 cm, at point [2], at a height lower than point [1]. How does the speed of the water change it flows from [1] to [2]?
(A) Speed increases.
(B) Speed remains the same.
(C) Speed decreases.
(D) (Not enough information is given to determine this.)

Correct answer: (B)

From the continuity equation, if the pipe maintains a constant cross-sectional area, then the speed does not change as it flows from point [1] to point [2]. (However, in this case since the height drops, such that according to Bernoulli's equation there is a pressure increase for the water as it flows from point [1] to point [2].) Students apparently were inclined to say that water automatically increases speed as it flows "downhill" (but in this case, water is confined to within a pipe, and must obey continuity), or that perhaps viscosity (not covered in this course) is a factor in slowing down the fluid.

Student responses
Sections 4987, 4988
(A) : 9 students
(B) : 8 students
(C) : 2 students
(D) : 0 students

[Version 2]

[3.0 points.] Water flows through a pipe with a speed of 0.80 m/s through a pipe of 2.0 cm inside radius, at point [1]. The pipe has the same radius of 2.0 cm, at point [2], at a height higher than point [1]. How does the speed of the water change it flows from [1] to [2]?
(A) Speed increases.
(B) Speed remains the same.
(C) Speed decreases.
(D) (Not enough information is given to determine this.)

Correct answer: (B)

From the continuity equation, if the pipe maintains a constant cross-sectional area, then the speed does not change as it flows from point [1] to point [2]. (However, in this case since the height increases, such that according to Bernoulli's equation there is a pressure decrease for the water as it flows from point [1] to point [2].) Students apparently were inclined to say that water automatically decreases speed as it flows "uphill" (but in this case, water is confined to within a pipe, and must obey continuity), or that perhaps viscosity (not covered in this course) is a factor in slowing down the fluid.

Student responses
Sections 4987, 4988
(A) : 1 student
(B) : 8 students
(C) : 7 students
(D) : 0 students

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