If water flows with a velocity of $20 \,cm \,s^{-1}$ in a pipe of radius $2 \,cm$, then the flow is (The coefficient of viscosity of water is $10^{-3} \,kg \,m^{-1} \,s^{-1}$ and density of water is $10^3 \,kg \,m^{-3}$).

$A$ dimensionally consistent relation for the volume $V$ of a liquid of coefficient of viscosity $\eta$ flowing per second through a tube of radius $r$ and length $l$ and having a pressure difference $p$ across its end,is

In deriving Bernoulli's equation,we equated the work done on the fluid in the tube to its change in the potential and kinetic energy.
$(a)$ What is the largest average velocity of blood flow in an artery of diameter $2 \times 10^{-3} \;m$ if the flow must remain laminar?
$(b)$ Do the dissipative forces become more important as the fluid velocity increases? Discuss qualitatively.

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

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 $p$.)

Show that the Reynolds number is dimensionless.