Water is conveyed through a uniform tube of $8 \text{ cm}$ in diameter and $3140 \text{ m}$ in length at the rate of $2 \times 10^{-3} \text{ m}^3/\text{s}$. The pressure required to maintain the flow is (Viscosity of water $= 10^{-3} \text{ SI units}$):

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?

$A$ 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 $m/s$)

Range of Reynolds number are given in Column - $I$ and types of flow are given in Column - $II$. Match them appropriately.

Column - $I$	Column - $II$
$(a)$ $R_e > 2000$	$(i)$ Streamline
$(b)$ $1000 < R_e < 2000$	$(ii)$ Turbulent
	$(iii)$ Unsteady

What is the value of Reynolds number for unsteady flow?

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: