Velocity distribution of a falling film with variable viscosity

Input(s)

ρ\rho: Density (kg/m3)\left(\mathrm{kg} / \mathrm{m}^{3}\right)

g: Gravitational Acceleration (m/s2)\left(\mathrm{m} / \mathrm{s}^{2}\right)

δ\delta: Film Thickness (m)

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

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

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

Output(s)

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

Formula(s)

vz=(ρ gδ2)cos(β)(1(xδ)2)2μ\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 .


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