Physics midterm question: constant pressure in widening, ascending pipe

Physics 205A Midterm 2, fall semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 9.43, 9.45

Water flows through a pipe that increases in cross-sectional area and elevation as it flows from point [1] to point [2]. Discuss how it is plausible that the water pressure remains constant as it flows from [1]→[2]. Explain your reasoning using the continuity equation, Bernoulli's equation, and the properties of ideal fluid flow.

Solution and grading rubric:

• p:
  Correct. Discusses/demonstrates the application of ideal fluid conservation laws:
  1. continuity, where the widening of the pipe at point [2] will have a corresponding slower speed;
  2. energy density (Bernoulli's equation), as the speed decreases (making the (1/2)·ρ·∆(v²) term negative) and the elevation increases (making the ρ·g·∆y term positive) for the fluid flowing from point [1] to point [2], it is plausible that these terms will together sum to zero, such that the ∆P term would also be zero.
• r:
  Nearly correct, but includes minor math errors.
• t:
  Nearly correct, but approach has conceptual errors, and/or major/compounded math errors. Understands that increasing elevation would decrease pressure (if speed remains constant), and increasing area would increase pressure (if elevation remains constant), but does not explicitly discuss how speed would decrease in the wider section of pipe (due to continuity).
• 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: midterm02veR1
p: 37 students
r: 8 students
t: 11 students
v: 9 students
x: 1 student
y: 0 students
z: 0 students

A sample "p" response (from student 1220):
A sample "t" response (from student 4455), not explicitly discussing the continuity equation: