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 $Q$?

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

If the pressure difference across a pipe of radius $r$ and length $l$ is $p$,then the volume of liquid flowing out per second is $V$. Find the correct expression for $V$.

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 $\rho$ is the density and $\eta$ is the coefficient of viscosity of a fluid which flows with a speed $v$ in a pipe of diameter $d$,the correct formula for Reynolds number $R_{e}$ is ..............

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]