Here is the problem: (From sabersky, problem 8.9)(adsbygoogle = window.adsbygoogle || []).push({});

Vapor condenses on a vertical surface to form a liquid film. The film moves under gravity and forms a laminar liquid boundary layer. Derive an expression for the mass flow rate dm/dt as a function of the local film thickness [itex]\delta[/itex]. Neglect any velocity components in the y-direction. (the positive x direction is down and y points away from the solid surface)

Answer: dm/dt=[itex]\rho g \delta^3/3 \nu [/itex], where [itex]\rho[/itex] is the density and [itex]\nu[/itex] is the kinematic viscosity.

I'm really stuck on this one. The continuity equation is useless because there must be vapor condensing on to the film (or else dm/dt would be constant). Assuming this vapor has no momentum, I was able to use the momentum equation to get:

[tex]\frac{\partial}{\partial x} \int_0^\delta \rho u^2 dy =-\tau_0+\rho g[/tex]

where [itex]\tau_0[/itex] is the shear force at the solid surface. Since g and [itex]\nu[/itex] appear not as a sum but as a product in the final answer, I assume there must be another equation relating them. Can anyone help me out here?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Boundary layer question

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**