The unit of the coefficient of viscosity in t | vedclass

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(D) The coefficient of viscosity $\eta$ is defined by the formula $F = \eta A \frac{dv}{dx}$,where $F$ is force,$A$ is area,and $\frac{dv}{dx}$ is the

Vedclass · Accepted Answer

$kg/(m \cdot s)$

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(D) The coefficient of viscosity $\eta$ is defined by the formula $F = \eta A \frac{dv}{dx}$,where $F$ is force,$A$ is area,and $\frac{dv}{dx}$ is the velocity gradient.Rearranging for $\eta$,we get $\eta = \frac{F}{A (dv/dx)}$.The dimensional formula for force $F$ is $[MLT^{-2}]$,for area $A$ is $[L^2]$,and for velocity gradient $dv/dx$ is $[T^{-1}]$.Substituting these into the formula: $[\eta] = \frac{[MLT^{-2}]}{[L^2][T^{-1}]} = [ML^{-1}T^{-1}]$.In the $S.I.$ system,the units are $kg$ for mass,$m$ for length,and $s$ for time.Therefore,the unit of the coefficient of viscosity is $kg \cdot m^{-1} \cdot s^{-1}$ or $kg/(m \cdot s)$.

The unit of the coefficient of viscosity in the $S.I.$ system is

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