$A$ liquid flows through a pipe with a pressure difference of $P$. What should be the pressure difference required to maintain the same flow rate if the radius is doubled and the length is doubled?

Two different liquids are flowing in two tubes of equal radius. The ratio of coefficients of viscosity of liquids is $52:49$ and the ratio of their densities is $13:1$,then the ratio of their critical velocities will be

$(a)$ 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 $2.084 \times 10^{-3} \; Pa \; s$).

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:

If it takes $5\,minutes$ to fill a $15\,litre$ bucket from a water tap of diameter $\frac{2}{\sqrt{\pi}}\,cm$,then the Reynolds number for the flow is (density of water $= 10^3\,kg/m^3$ and viscosity of water $= 10^{-3}\,Pa\cdot s$) close to

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