Average velocity of a falling film with variable viscosity

Input(s)

$\rho$: Density $(\mathrm{g} / \mathrm{cc})$

g: Acceleration due to Gravity $\left(\mathrm{cm} / \mathrm{s}^{2}\right)$

$\boldsymbol{\delta}$: Film Thickness $(\mathrm{cm})$

$\beta$: Inclination (rad)

$\mu$: Viscosity $(\mathrm{cP})$

$\boldsymbol{x}$: Position in Film $(\mathrm{cm})$

Output(s)

$v$: Velocity $(\mathrm{cm} / \mathrm{s})$

Formula(s)

$$ v=\left(\frac{\rho * g *\left(\delta^{2}\right) * \cos (\beta)}{2 * \mu}\right) *\left(1-\left(\frac{x}{\delta}\right)^{2}\right) $$

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley \& Sons., Chapter: 2, Page: 48.