Average velocity over the cross section of a falling film

Input(s)

$\rho$: Density $\left(\mathrm{kg} / \mathrm{m}^{3}\right)$

g: Gravitational Acceleration $\left(\mathrm{m} / \mathrm{s}^{2}\right)$

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

$\mu$: Viscosity $(\mathrm{kg} /(\mathrm{ms}))$

$\beta$: Angle of Inclination w.r.t Direction of Gravity (rad)

$v_{z, \text { max }}$: The Maximum Velocity at $\mathrm{x}=0(\mathrm{~m} / \mathrm{s})$

Output(s)

$v_{z}$: Average Velocity $(\mathrm{m} / \mathrm{s})$

Formula(s)

$$ v_{z}=\frac{\rho * g * \delta^{2} * \cos (\beta)}{3 * \mu} $$

Reference(s)

Bird, R.B., Stewart, W.E., and Lightfoot, E.N. (2002). Transport Phenomena (Second ed.). John Wiley \& Sons, Chapter: 2, Page: 45.