Physics quiz question: speed, pressure changes in horizontal, narrowing pipe

Physics 205A Quiz 5, fall semester 2017
Cuesta College, San Luis Obispo, CA

Water as it moves horizontally from [1]→[2] through a pipe with decreasing cross-sectional area. The radius of the pipe at point [1] is 0.10 m, and water enters point [1] with a speed of 0.25 m/s. Assume ideal fluid flow. As water flows from [1]→[2], the speed __________; while the pressure __________.
(A) remains constant; remains constant.
(B) remains constant; changes.
(C) changes; remains constant.
(D) changes; changes.

Correct answer (highlight to unhide): (D)

From applying the continuity equation:

A₁·v₁ = A₂·v₂,

because the diameter of the pipe narrows as it flows from [1]→[2], the cross-sectional area decreases (A₁ > A₂), such that the speed of the water increases:

v₁ < v₂.

Then from Bernoulli's equation:

0 = ∆P + (1/2)·ρ·∆(v²) + ρ·g·∆y,

the third term on the right-hand side is zero because there is no change in elevation (y₁ = y₂), while the second term on the right-hand side increases (as the speed increases along the pipe), thus the pressure must decrease. Thus both speed and pressure change as water flows from [1]→[2] through this pipe.

Sections 70854, 70855
Exam code: quiz05nWaW
(A) : 0 students
(B) : 6 students
(C) : 6 students
(D) : 36 students

Success level: 73%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.29