Graduate Should the boundary condition have to satisfy dimensional consistency?

[SaleemKU]

Should the boundary condition have to satisfy dimensional consistency?

 

[BvU]

Yes

 

[SaleemKU]

But we see papers and exercise, normally B.C.s look not consistence dimensionally. for example v(r,t)= U*t^p, where U is constant velocity and p is positive no.?

 

[renormalize]

But we see papers and exercise, normally B.C.s look not consistence dimensionally. for example v(r,t)= U*t^p, where U is constant velocity and p is positive no.?

Can you cite a specific explicit example for us to examine?

 

[BvU]

v(r,t)= U*t^p, where U is constant velocity and p is positive no.

Looks as if the exercise composer is a little bit sloppy. Can you post the complete exercise ?

https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

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[pasmith]

But we see papers and exercise, normally B.C.s look not consistence dimensionally. for example v(r,t)= U*t^p, where U is constant velocity and p is positive no.?

For the purpose of this exercise, does it make a difference to the mathematical analysis if the boundary condition is the dimensionally consistent kUt^p or U(t/t_0)^p rather than sloppy Ut^p?

It is common to use scaled units in order sweep such constants of proportionality under the carpet. The result is that expressions might look dimensionally inconsistent at first glance, but in truth at this stage every quantity is now dimensionless.

 

[fresh_42]

Should the boundary condition have to satisfy dimensional consistency?

I like to think of differential equations as vector fields, e.g., the predator-prey system,

The initial conditions determine where you start your flow through such a vector field. Hence, they have the same dimensions such a starting point has in phase space.