Question

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

• A. $x=y$
• B. $x=-y$
• C. $y^2=x$
  
• D. $y=-x^2$

Answer 1

The correct option is B $x=-y$

$\left[m\right]=\left[P{]}^x\right[v{]}^y$
$\left[M{L}^{-2}{T}^{-1}\right]=\left[M{L}^{-1}{T}^{-2}{]}^x\right[L{T}^{-1}{]}^y$
$\left[M{L}^{-2}{T}^{-1}\right]=\left[M^x{L}^{-x+y}{T}^{-2x-y}\right]$
$\to x=1,-x+y=-2$
$y=-2+1$
$=-1$
$\to x=-y$