Physics quiz question: different densities in a U-tube

Physics 5A Quiz 5, Spring Semester 2008
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 1/e, Multiple-Choice Question 9.9, Problem 9.24

[3.0 points.] A manometer contains two different fluids of different densities. Both sides are open to the atmosphere. Which location has the greater absolute pressure?
(A) Location [1].
(B) Location [2].
(C) (Both locations have the same absolute pressure.)
(D) (Not enough information is given to determine this.)

Correct answer: (A)

Consider the fluid pressure at location [A], the interface between the darker fluid and the lighter fluid in the left side of the U-tube. This is the same pressure as location [B], in the lighter fluid in the right side of the U-tube, thus P_A = P_B. Then with d as the depth from locations [1] and [2] down to locations [A] and [B]:

P_A = P_B,
P_1 + rho_dark*g*d = P_2 + rho_light*g*d.

However, since the darker fluid has a lighter density than that of the darker fluid, rho_dark < rho_light, such that P_1 > P_2.

Student responses
Sections 4987, 4988
(A) : 12 students
(B) : 15 students
(C) : 7 students
(D) : 0 students