F=ma 2024 Problem 15

Physics · mechanics

Problem

Question: The viscous force between two plates of area AA, with relative speed vv and separation dd, is F=ηAv/dF = {\eta Av}/d, where η\eta is the viscosity. In fluid mechanics,the Ohnesorge number is a dimensionless number proportional to η\eta which characterizes the importance of viscous forces,in a drop of fluid of density ρ\rho, surface tension γ\gamma, and length scale ℓ\ell. Which of the following could be the definition of the Ohnesorge number? (A) ηℓργ\frac{\eta \ell}{\sqrt{\rho \gamma}}. (B) ηℓργ\eta \ell \sqrt{\frac{\rho}{\gamma}}. (C) ηργℓ\eta \sqrt{\frac{\rho}{\gamma \ell}}. (D) ηρℓγ\eta \sqrt{\frac{\rho \ell}{\gamma}}. (E) ηργℓ\frac{\eta}{\sqrt{\rho \gamma \ell}}.

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