The Asymptotic Laws of Freely-Ascending Convective Flows

The Asymptotic Laws of Freely-Ascending Convective Flows 

The jet is directed along the x-axis, u is the velocity, P1 is the momentum of the jet per unit length of the slit, and P2 is the full momentum of the round jet. The functions f1 and /2 are found by integration of the ordinary differential equations. The result is in satisfactory agreement with experiment. 

Schlichting [2] used an analogous method to study the laminar diffusion of a jet where he obtained 

In the present note we use the same methods to find similar expressions for convective flows freely-ascending under the action of gravity and density differences. We direct the x-axis upward in the direction of the flow. Instead of conservation of momentum (which will not exist because of the action of buoyancy forces), we write the conservation of heat flux 

We assume that on every horizontal plane the pressure is the same everywhere we determine the value dp/dx from the value of dp/dx = —gp0 at infinity (for y — oo). 

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