The mass of a liquid flowing per second per u | vedclass

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(B) The mass flow rate per unit area is given by $\frac{M}{A t} \propto P^{x} v^{y}$.The dimensional formula for mass per unit area per unit time is $

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$x = -y$

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(B) The mass flow rate per unit area is given by $\frac{M}{A t} \propto P^{x} v^{y}$.The dimensional formula for mass per unit area per unit time is $[M L^{-2} T^{-1}]$.The dimensional formula for pressure $P$ is $[M L^{-1} T^{-2}]$ and for velocity $v$ is $[L T^{-1}]$.Equating the dimensions on both sides:$[M L^{-2} T^{-1}] = [M L^{-1} T^{-2}]^x [L T^{-1}]^y$$[M L^{-2} T^{-1}] = M^x L^{-x+y} T^{-2x-y}$Comparing the powers of $M, L,$ and $T$:For $M$: $x = 1$For $L$: $-x + y = -2$For $T$: $-2x - y = -1$Substituting $x = 1$ into the equation for $L$: $-1 + y = -2 \Rightarrow y = -1$.Since $x = 1$ and $y = -1$,we have $x = -y$.

The mass of a liquid flowing per second per unit area of cross section of a tube is proportional to $P^x$ and $v^y$,where $P$ is the pressure difference and $v$ is the velocity. Then,the relation between $x$ and $y$ is

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