20161125

Physics midterm question: increasing pressure in horizontal, widening pipe?

Physics 205A Midterm 2, fall semester 2016
Cuesta College, San Luis Obispo, CA

A Physics 205A student asked the following question on an online reading assignment[*]:
Can pressure increase as the radius of a pipe with flowing water increases?
Discuss a plausible horizontal pipe system that would result in this happening. Explain your reasoning using the continuity equation, Bernoulli's equation, and the properties of ideal fluid flow.

[*] waiferx.blogspot.com/2016/10/online-reading-assignment-ideal-fluid.html.

Solution and grading rubric:
  • p:
    Correct. Discusses/demonstrates the application of ideal fluid conservation laws for a horizontal pipe with a narrow cross-section at point [1] and a wider cross-section at point [2]:
    1. continuity, where the widening of the pipe at point [2] will cause a corresponding slower speed there;
    2. energy density (Bernoulli's equation), as the speed decreases (making the (1/2)⋅ρ⋅Δ(v2) term negative) and the elevation is not changing (making the ρ⋅g⋅Δy term zero) for the fluid flowing from point [1] to point [2], then in order for all three terms on the right-hand side of Bernoulli's equation to sum to zero, the ΔP term would need to be positive, and thus pressure would increase flowing from point [1] to point [2].
  • r:
    Nearly correct, but includes minor math errors.
  • t:
    Nearly correct, but approach has conceptual errors, and/or major/compounded math errors.
  • v:
    Implementation of right ideas, but in an inconsistent, incomplete, or unorganized manner. Some garbled attempt at applying continuity and Bernoulli's equation.
  • x:
    Implementation of ideas, but credit given for effort rather than merit. Approach other than that of applying continuity and Bernoulli's equation.
  • y:
    Irrelevant discussion/effectively blank.
  • z:
    Blank.
Grading distribution:
Sections 70854, 70855, 73320
Exam code: midterm02oPt0
p: 36 students
r: 4 students
t: 9 students
v: 3 students
x: 4 students
y: 0 students
z: 0 students

A sample "p" response (from student):

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