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 $= 10^{-3} \text{ SI units}$):

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 $....V$

If $R_e > 2000$,then which type of flow exists? Explain.

$A$ horizontal pipeline carrying gasoline has a cross-sectional diameter of $5 \,mm$. If the viscosity and density of the gasoline are $6 \times 10^{-3} \,Poise$ and $720 \,kg/m^3$ respectively, the velocity after which the flow becomes turbulent is:

What is Reynolds number?

$A$ 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 $m/s$)