Physics quiz question: pressure change in elevated oil pipeline

Physics 205A Quiz 5, fall semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 9.45

"Trans-Alaska Pipeline"
U.S. Government, Public Domain (PD-USGOV) image
commons.wikimedia.org/wiki/File:Trans-Alaska_Pipeline.jpg

Oil (density 8.6×10² kg/m³) in the Trans-Alaskan pipeline[*] with a diameter of 1.2 m flows at a speed of 
0.94 m/s. Assume ideal fluid flow. The pressure of the oil __________ as it rises in the photo shown above.
(A) decreases.
(B) remains constant.
(C) increases.
(D) (Not enough information is given.)

[*] Trans Alaska Pipeline System--The Facts, Alyeska Pipeline Service Company (2013), alyeska-pipe.com/assets/uploads/pagestructure/NewsCenter_MediaResources_FactSheets_Entries/635078372894251917_2013AlyeskaTAPSFactBook.pdf.

Correct answer (highlight to unhide): (A)

From applying the continuity equation:

A₁·v₁ = A₂·v₂,

because the diameter of the pipeline is constant, the cross-sectional area remains constant (A₁ = A₂), such that the speed of the oil is constant:

v₁ = v₂.

Then from Bernoulli's equation:

0 = ∆P + (1/2)·ρ·∆(v²) + ρ·g·∆y,

the second term on the right-hand side is zero because there is no change in the speed of the fluid, while the third term on the right-hand side increases (as the elevation increases along the pipe), thus the pressure must decrease as oil flows into the higher section of pipe.

Sections 70854, 70855, 73320
Exam code: quiz05mRp4
(A) : 24 students
(B) : 20 students
(C) : 19 students
(D) : 1 student

Success level: 38%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.33