Physics quiz question: water pressure at bottom of graduated cylinder

Physics 205A Quiz 5, fall semester 2017
Cuesta College, San Luis Obispo, CA

A graduated cylinder is filled with 10 cm of water. The top of the water level is exposed to atmospheric pressure (P_atm = 101.3 kPa). The density of water is ρ_water = 1.00×10³ kg/m³. The water pressure at the bottom of graduated cylinder is:
(A) 1.0×10² Pa.
(B) 9.8×10² Pa.
(C) 1.003×10⁵ Pa.
(D) 1.023×10⁵ Pa.

Correct answer (highlight to unhide): (D)

For static fluids, the energy density relation between pressure and changes in elevation is given by:

0 = ∆P + ρ·g·∆y,

0 = (P_bottom – P_top) + ρ_water·g·(y_bottom – y_top),

where the air pressure at the water surface at the top of the graduated cylinder is 101.3 kPa = 1.013×10⁵ Pa, such that:

P_bottom = P_top – ρ_water·g·(y_bottom – y_top),

P_bottom = 1.013×10⁵ Pa – (1.00×10³ kg/m³)·(9.80 m/s²)·((–0.10 m) – (0 m)),

P_bottom = 1.013×10⁵ Pa – 0.0098×10⁵ Pa = 1.023×10⁵ Pa.

(Response (A) is ρ_water·∆y; response (B) is ρ_water·g·∆y, which is the relative pressure difference between the top and bottom of the water in the graduated cylinder; response (C) is P_top + ρ_water·g·(y_bottom – y_top).)

Sections 70854, 70855
Exam code: quiz05nWaW
(A) : 2 students
(B) : 11 students
(C) : 15 students
(D) : 21 students

Success level: 43%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.28