Cuesta College, San Luis Obispo, CA
Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problem 9.45
U.S. Government, Public Domain (PD-USGOV) image
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.
(B) remains constant.
(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 as it moves from rises, the cross-sectional area remains constant, such that the speed of the oil is constant, thus:
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