Give the dimensional formula of the coefficie | vedclass

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Question

(A) The coefficient of viscosity $\eta$ is defined by Newton's law of viscosity: $F = -\eta A \frac{dv}{dx}$.Rearranging for $\eta$,we get $\eta = \fr

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) The coefficient of viscosity $\eta$ is defined by Newton's law of viscosity: $F = -\eta A \frac{dv}{dx}$.Rearranging for $\eta$,we get $\eta = \frac{F}{A (dv/dx)}$.The dimensional formula for force $F$ is $[M^1 L^1 T^{-2}]$.The dimensional formula for area $A$ is $[L^2]$.The dimensional formula for velocity gradient $dv/dx$ is $[L T^{-1}] / [L] = [T^{-1}]$.Substituting these into the formula: $\eta = \frac{[M^1 L^1 T^{-2}]}{[L^2] [T^{-1}]} = [M^1 L^{-1} T^{-1}]$.Thus,the dimensional formula of the coefficient of viscosity is $M^1 L^{-1} T^{-1}$.

Give the dimensional formula of the coefficient of viscosity.

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