Physics quiz question: exit speed of water flow

Physics 205A Quiz 5, fall semester 2018
Cuesta College, San Luis Obispo, CA

Water enters point [1] with a speed of 0.80 m/s. The pipe at point [2] is at a lower height than point [1], and has twice the cross-sectional area. Assume ideal fluid flow. The speed of the water at point [2] is:
(A) 0.40 m/s.
(B) 0.57 m/s.
(C) 0.80 m/s.
(D) 1.6 m/s.

Correct answer (highlight to unhide): (A)

From applying the continuity equation:

A₁·v₁ = A₂·v₂,
where the fluid volume flow rate is the same throughout this section of pipe.
As the cross-sectional area of the pipe widens by a factor of two as it flows from [1]→[2], 2·A₁ = A₂, such that the speed of the water at point [2] is then:

A₁·v₁ = (2·A₁)·v₂,

(1/2)·v₁ = v₂,

such that the speed at point [2] is 0.40 m/s, half the speed at point [1].

(Response (B) is (v₁/√(2); response (C) is v₁; response (D) is 2·v₁.)

Sections 70854, 70855
Exam code: quiz05Ro74
(A) : 32 students
(B) : 3 students
(C) : 8 students
(D) : 9 students

Success level: 62%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.38