Hello,

I have a very simple question: If gravity is there in, say, y-component of the NS-equation, can I solve its non-dimensional form and port it to other similar problems?!

DEL_v over DEL_t + u.DEL_v/DEL_x + v.DEL_v/DEL_y = -(1/rho).DEL_P/DEL_y + nu.(DEL^2 v) - g : Dimensional Form

DEL_v* over DEL_t* + u*.DEL_v*/DEL_x* + v*.DEL_v*/DEL_y* = -DEL_P*/DEL_y* + (1/Re).(DEL^2 v*) - (L/V0^2)g : NON-dimensional Form

As we can see in the 2nd equation,it contains "Re" as well as (L/v0^2). If "Re" and (L/v0^2), BOTH are same for any two similar problems, only then solution of this non-dimensional equations seems to be useful?!!

Could any of you please confirm it?

Thank you,

-Chandra

The second similarity parameter you found is the reciprocal of the Froude number squared: Fr = V0/sqrt(gL).

Dynamic similarity is achieved if you match Re and Fr.

if there are two geometrically similar systems with similar boundary conditions (non-dimensional) at the same geometrical correspondence, the two systems will have the same non-dimensional quantities like Re, Fr, u*, v*, delp*/dely* etc. hence if the equations are solved in non-dimensional form, the specific advantage is that irrespective of the properties etc of the fluids in the two apparently different systems (dimensional form), velocity, pressure etc profiles (non-dim) will be same. this helps in validating results when say experimental results are available for different fluids and/or different flow conditions. this also helps in scale up.

Thank you very much to both of you. It helped me a lot to have understanding of it.

Thank you,

-Chandra