When a liquid flows through a tube,the Reynolds number is $900$. The flow of the liquid is:

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

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 $....V$

$(a)$ What is the largest average velocity of blood flow in an artery of radius $2 \times 10^{-3} \; m$ if the flow must remain laminar?
$(b)$ What is the corresponding flow rate? (Take viscosity of blood to be $2.084 \times 10^{-3} \; Pa \; s$).

We have two narrow capillary tubes $T_1$ and $T_2$. Their lengths are $l_1$ and $l_2$ and radii of cross-section are $r_1$ and $r_2$ respectively. The rate of flow of water under a pressure difference $P$ through tube $T_1$ is $8 \ cm^3/sec$. If $l_1 = 2l_2$ and $r_1 = r_2$,what will be the rate of flow when the two tubes are connected in series and the pressure difference across the combination is the same as before $(= P)$?

$A$ 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 ......... $\%$