Water flows in a streamline manner through a capillary tube of radius $a$. The pressure difference is $P$ and the rate of flow is $Q$. If the radius is reduced to $\frac{a}{4}$ and the pressure is increased to $4P$,then the rate of flow becomes ................

Two capillary tubes of the same radius but lengths $l_1$ and $l_2$ are connected in parallel at the bottom of a vessel. What should be the length of a single capillary tube of the same radius that replaces both,such that the flow rate remains the same?

What is the value of the Reynolds number $(R_e)$ for unsteady flow?

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 ..............

The rate of steady volume flow of water through a capillary tube of length $l$ and radius $r$,under a pressure difference of $p$ is $V$. This tube is connected with another tube of the same length but half the radius,in series. Then,the rate of steady volume flow through them is (The pressure difference across the combination is $p$.)

Which of the following quantities has the dimensions of $\frac{\pi P r^4}{8 Q l}$? (Where $P =$ pressure,$r =$ radius,$Q =$ volume flow rate in $m^3/s$,and $l =$ length.)