Question

The volume of a liquid (v) flowing per second through a cylindrical tube depends upon the pressure gradient (p/l) radius of the tube (r) coefficient of viscosity ($\eta$) of the liquid by dimensional method the correct formula is

• A. $V\alpha \frac{P{r}^4}{\eta l}$
• B. $V\alpha \frac{Pr}{\eta l^4}$
• C. $V\alpha \frac{P{l}^4}{\eta r}$
• D. $None$

Answer 1

The correct option is C $V\alpha \frac{P{l}^4}{\eta r}$

$V\propto R^a{\left(\frac{P}{L}\right)}^b{\eta }^c$

$V=\left[L{]}^3\right[T{]}^{-1}$

$R=\left[L\right]$

$\frac{P}{L}=\left[M\right]\left[T{]}^{-2}\right[L{]}^{-2}$

$\eta =\left[M\right]\left[T{]}^{-1}\right[L{]}^{-1}$

$\Rightarrow \left[L{]}^3\right[T{]}^{-1}=\left[L{]}^a\right[M{]}^b\left[T{]}^{-2b}\right[L{]}^{-2b}\left[M{]}^c\right[L{]}^{-c}[T{]}^{-c}$

$a-2b-c=3$

$b+c=0$

$-2b-c=-1$

$a=4,b=1,c=-1$

$V\propto \frac{P{R}^4}{\eta L}$