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 $....V$

$A$ pure number which determines the type of flow of a liquid through a pipe is known as

If it takes $5\,minutes$ to fill a $15\,litre$ bucket from a water tap of diameter $\frac{2}{\sqrt{\pi}}\,cm$,then the Reynolds number for the flow is (density of water $= 10^3\,kg/m^3$ and viscosity of water $= 10^{-3}\,Pa\cdot s$) close to

If $\rho$ is the density and $\eta$ is the coefficient of viscosity of a fluid which flows with a speed $v$ in a pipe of diameter $d$,the correct formula for Reynolds number $R_{e}$ is ..............

Glycerine flows steadily through a horizontal tube of length $1.5 \; m$ and radius $1.0 \; cm$. If the amount of glycerine collected per second at one end is $4.0 \times 10^{-3} \; kg \; s^{-1}$,what is the pressure difference between the two ends of the tube? (Density of glycerine $= 1.3 \times 10^{3} \; kg \; m^{-3}$ and viscosity of glycerine $= 0.83 \; Pa \; s$). [You may also like to check if the assumption of laminar flow in the tube is correct]

Two capillary tubes of the same length but different radii $r_1$ and $r_2$ are fitted in parallel to the bottom of a vessel. The pressure head is $P$. What should be the radius of a single tube that can replace the two tubes so that the rate of flow is the same as before?