Physics midterm question: descending, widening pipe

Physics 205A Midterm 2, fall semester 2012
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 9.41, 9.45

The pressure of water __________ as it flows from point [1] to point [2]. (Assume ideal fluid flow.)
(A) decreases.
(B) remains constant.
(C) increases.
(D) (Not enough information is given.)

Correct answer (highlight to unhide): (C)

From applying the continuity equation:

A₁·v₁ = A₂·v₂,

the water speed at point [2] is slower than at point [1], because the cross-sectional area at point [2] is larger than at point [1].

Then from Bernoulli's equation:

0 = ∆P + (1/2)·ρ·∆(v²) + ρ·g·∆y,

the second term on the right-hand side decreases due to the decrease in speed from point [1] to point [2], while the third term on the right-hand side decreases (as the elevation decreases along the pipe), thus the pressure must increase as water flows from point [1] to point [2].

Sections 70854, 70855
Exam code: midterm02gL0u
(A) : 21 students
(B) : 5 students
(C) : 26 students
(D) : 1 student

Success level: 48%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.26