Two capillary tubes of same length each of $50 \ cm$ but of different radii $4 \ mm$ and $2 \ mm$ are connected in series. When water flows,the pressure difference between the ends of the arrangement is $P$. Then the pressure difference between the ends of the first tube is

In which one of the following cases will the liquid flow in a pipe be most streamlined?

Two liquids of densities $d_1$ and $d_2$ are flowing in identical capillary tubes under the same pressure difference. If $t_1$ and $t_2$ are the times taken for the flow of equal quantities (mass) of liquids,then the ratio of the coefficient of viscosity of the liquids must be:

What is the value of Reynolds number for streamline flow?

Consider a steady flow of oil in a pipeline. The cross-sectional radius of the pipeline decreases gradually as $r = r_0 e^{-\alpha x}$, where $\alpha = \frac{1}{3} \text{ m}^{-1}$ and $x$ is the distance from the pipeline inlet. If $R_1$ is the Reynolds number for a certain pipeline cross-section at a distance $x_1$ metre from the inlet and $R_2$ is for distance $(x_1 + 3)$ metre, then the ratio $\frac{R_1}{R_2}$ is

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