Question

The mass of the liquid flowing per second per unit area of cross-section of the tube is proportional to (pressure difference across the ends)${}^n$ and (average velocity of the liquid )${}^m.$ Which of the following relations between $m$ and $n$ is correct ?

• A. $m=n$
• B. $m=-n$
• C. $m^2=n$
• D. $m={-n}^2$

Answer 1

Answer: (B)

$m=-n$

$\left[M/At\right]={[P}^n].[v^m]$

or, $[M.L^{-2}.T^{-2}]={\left[M{L}^{-1}{T}^{-2}\right]}^n.{\left[L{T}^{-1}\right]}^m$
$\Rightarrow$ $n=1,m-n=-2$
or, $m=-1$
$\therefore$ $m=-n$