When a liquid of density $\rho$ flows through a tube of diameter $d$ with critical velocity $V$,then the Reynolds number is (where $\eta$ is the coefficient of viscosity of the liquid).

The rate of flow of water in a capillary tube of length $\ell$ and radius $r$ is $V.$ The rate of flow in another capillary tube of length $2 \ell$ and radius $2 r$ for the same pressure difference would be $....V$

What is critical velocity? Write its equation.

Two tubes of radii $r_1$ and $r_2$,and lengths $l_1$ and $l_2$,respectively,are connected in series and a liquid flows through each of them in streamline conditions. $P_1$ and $P_2$ are pressure differences across the two tubes. If $P_2 = 4P_1$ and $l_2 = \frac{l_1}{4}$,then the radius $r_2$ will be equal to:

$A$ liquid of density $10^3 \, kg/m^3$ and coefficient of viscosity $8 \times 10^{-2} \, \text{decapoise}$ is flowing in a tube of radius $2 \, cm$ with speed $2 \, m/s$. The Reynold's number is ..........

Show that the Reynolds number is dimensionless.