Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 9.50
[3.0 points.] Water at point [1] flows with a speed of 0.75 m/s through a pipe of 0.20 m inner radius. The pipe at point [2] tapers down to an inner radius of 0.050 m. Assume ideal fluid flow. The pressure of the water __________ as it flows from point [1] to point [2]. (A) decreases.
(B) increases.
(C) remains constant.
(D) (Not enough information is given.)
Correct answer: (A)
From applying the continuity equation:
A_1*v_1 = A_2*v_2,
the water speed at point [2] is greater than at point [1], because the cross-sectional area at point [2] is smaller than at point [1].
Then from Bernoulli's equation:
0 = delta(P) + (1/2)*rho*delta(v^2) + rho*g*delta(y),
the kinetic head (the second term on the right-hand side) increases due to the increase in speed from point [1] to point [2], while the gravitational head (the third term on the right-hand side) remains constant due to no change in elevation along the horizontal pipe, thus the pressure must decrease as water flows from point [1] to point [2].
Student responses
Sections 30880, 30881
(A) : 22 students
(B) : 16 students
(C) : 1 student
(D) : 0 students
"Difficulty level": 56%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.65
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