I will derive the Reynolds Number denoting all the variables along the way
$A \rightarrow$ Area of cross section of tube
$v \rightarrow$ Velocity of fluid flow in tube
$\rho \rightarrow$ Density of fluid in tube
$r \rightarrow$ Radius of tube
$\eta \rightarrow$ Coefficient of viscosity
Mass of fluid flowing per second = $\mu$ = $\rho Av$
Inertial force = Force due to change in momentum = $\Delta l$= $\mu \cdot v$ = $\rho Av^2$
Viscous force = $F$ = $\eta \frac{Av}{r}$
Reynolds Number = $\frac{\Delta l}{F} = \frac{\rho A v^2}{\eta \frac{Av}{r}} = \frac{\rho A v^2 r}{\eta A v}$
Now this is of the form that was given in NCERT. which means that $A$ was cross sectional area after all.