Stokes' law states that the viscous drag force $F$ experienced by a sphere of radius $a$,moving with a speed $v$ through a fluid with coefficient of viscosity $\eta$,is given by $F=6 \pi \eta a v$. If this fluid is flowing through a cylindrical pipe of radius $r$,length $l$ and a pressure difference of $p$ across its two ends,then the volume of water $V$ which flows through the pipe in time $t$ can be written as $\frac{V}{t}=k\left(\frac{p}{l}\right)^a \eta^b r^c$,where $k$ is a dimensionless constant. The correct values of $a, b$ and $c$ are

• A
  $a=1, b=-1, c=4$
• B
  $a=-1, b=1, c=4$
• C
  $a=2, b=-1, c=3$
• D
  $a=1, b=-2, c=-4$