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.