The rate of steady volume flow of water through a capillary tube of length $l$ and radius $r$,under a pressure difference of $p$ is $V$. This tube is connected with another tube of the same length but half the radius,in series. Then,the rate of steady volume flow through them is (The pressure difference across the combination 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]

Under a pressure head,the rate of orderly volume flow of a liquid through a capillary tube is $Q$. If the length of the capillary tube is doubled and the diameter of the tube is halved,the rate of flow would become:

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:

For which of the following Reynolds numbers is a flow considered streamlined (laminar)?

The rate of flow of liquid in a tube of radius $r$ and length $l$,whose ends are maintained at a pressure difference $P$,is given by $V = \frac{\pi Q P r^4}{\eta l}$,where $\eta$ is the coefficient of viscosity. What is the value of $Q$?