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 .