In the case of a fluid flowing on a horizontal surface, the flow of the fluid becomes unsteady when the Reynolds number $(R_n)$ is:

Show that the Reynolds number is dimensionless.

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:

$A$ capillary tube of length $l$ and radius $r$ is connected to the bottom of a container. When the pressure difference across it is $P$,the volume of water flowing out per second is $V$. If another capillary tube of the same length but half the radius is connected in series with the first one,what will be the new volume of liquid flowing out per second? (The total pressure difference across the system is $P$.)

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]

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