Velocity distribution of a falling film with variable viscosity

Input(s)

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

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

$\delta$: Film Thickness (m)

$\mathrm{x}$: Distance in Cartesian Coordinate (x)

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

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

Output(s)

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

Formula(s)

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

Reference(s)

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