Dimensions of the coefficient of viscosity ar | vedclass

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Question

(C) The viscous force $F$ acting on a fluid layer is given by Newton's law of viscosity: $F = -\eta A \frac{dv}{dx}$.Here,$F$ is the force,$\eta$ is t

Vedclass · Accepted Answer

$M L^{-1} T^{-1}$

Vedclass · Answer

(C) The viscous force $F$ acting on a fluid layer is given by Newton's law of viscosity: $F = -\eta A \frac{dv}{dx}$.Here,$F$ is the force,$\eta$ is the coefficient of viscosity,$A$ is the area,and $\frac{dv}{dx}$ is the velocity gradient.Rearranging for $\eta$: $\eta = \frac{F}{A (dv/dx)}$.Substituting the dimensions: $[F] = [M L T^{-2}]$,$[A] = [L^2]$,$[dv] = [L T^{-1}]$,and $[dx] = [L]$.Thus,$[\eta] = \frac{[M L T^{-2}]}{[L^2] [L T^{-1} / L]} = \frac{[M L T^{-2}]}{[L^2] [T^{-1}]} = [M L^{-1} T^{-1}]$.Therefore,the correct option is $C$.

Dimensions of the coefficient of viscosity are

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