Physics quiz question: fluid surface tension

Physics 205A Quiz 1, fall semester 2018
Cuesta College, San Luis Obispo, CA

The Weber number W is a dimensionless physical constant used to characterize the behavior of flowing fluids[*]:

W = ρ·v²·D/σ.

The fluid density ρ is measured in units of kg·m^–3, the fluid velocity v is measured in units of m·s^–1, and the diameter of fluid droplets D is measured in units of m. The units for the fluid surface tension σ are:
(A) kg·s.
(B) kg·s^–2.
(C) kg·m·s^–1.
(D) kg·m^–6·s^–2.

[*] wki.pe/Weber_number.

Correct answer (highlight to unhide): (C)

Starting with the expression for Weber number W:

W = ρ·v²·D/σ,

the fluid surface tension σ can be expressed as:

σ = ρ·v²·D/W.

Then replacing the quantities in the equation with their kg, m and s units (and W is a dimensionless physical constant with no units), the units of σ are:

σ = kg·m^–3·(m·s^–1)²·m,

σ = kg·m^–3·m²·s^–2·m,

σ = kg·s^–2.

Sections 70854, 70855
Exam code: quiz01CrR4
(A) : 7 students
(B) : 46 students
(C) : 5 students
(D) : 3 students

Success level: 74%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.60