Water flows in a streamlined manner through a capillary of radius $a$,the pressure difference being $p$ and the rate of flow $Q$. If the radius is reduced to $a/2$ and the pressure is increased to $4p$,the rate of flow becomes:

Three capillaries of length $L, L/2$ and $L/3$ are connected in series. Their radii are $r, r/2$ and $r/3$ respectively. If stream-line flow is to be maintained and the pressure difference across the first capillary is $P$,then:

The volume of a liquid is proportional to......,given its density $\rho$,viscosity $\eta$ and $t$ the time of flow through a capillary tube of length $L$ and radius $R$,with a pressure difference $p$ across its ends.

$A$ capillary tube is attached horizontally to a constant head arrangement. If the radius of the capillary tube is increased by $10\%$,then the rate of flow of liquid will change nearly by ......... $\%$

$A$ glass tube of uniform cross-section is connected to a tap with a rubber tube. The tap is opened slowly. Initially, the flow of water in the tube is streamline. The speed of flow of water to convert it into a turbulent flow is (radius of tube $= 1 \,cm$, $\eta = 1 \times 10^{-3} \,Ns/m^2$, $R_{n} = 2500$, and density of water $\rho = 10^3 \,kg/m^3$) (in $m/s$)

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