Physics quiz question: cross-sectional area of pipe

Physics 205A Quiz 5, fall semester 2013
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 9.43(b)

Water at point [1] flows with a speed of 
3.0 m/s and a volume flow rate of 0.40 m³/s. The pipe at point [2] 
is four times the cross-sectional area of point [1]. Assume ideal 
fluid flow. The cross-sectional area of the pipe at point [1] is:
(A) 0.13 m².
(B) 1.2 m².
(C) 4.5 m².
(D) 7.5 m².

Correct answer (highlight to unhide): (A)

The definition of volume flow rate is:

(∆V/∆t) = A·v,

where A is the cross-sectional area of the pipe, and v is the speed of the fluid at that same location, such that:

A = (∆V/∆t)/v = (0.40 m³/s)/(3.0 m/s) = 0.13333333... m²,

or to two significant figures, the cross-sectional area at point [1] is 0.13 m².

(Response (B) is (∆V/∆t)·v; response (C) is (1/2)·v²; response (D) is v/(∆V/∆t).)

Sections 70854, 70855, 73320
Exam code: quiz05LuF7
(A) : 34 students
(B) : 20 students
(C) : 4 students
(D) : 3 students

Success level: 69%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.40