how does roughness adjustment changes value of hazen william roughness coefficient?

As roughness increases, Hazen-Williams coefficient drops. The amount and rate of drop depends on pipe material, water corrosivity, and time and is very system specific.

I am looking for mathematical relationship by which WaterCAD change the result if i do some roughness adjustment.

If i do roughness adjustment does it change the 'C' value, if yes by what factor, if no then what does it change.

There is no property called "roughness" in WaterGEMS. If you chose Hazen-Williams in the calculation options, you adjust C; if you chose Darcy-Weisbach, you adjust Darcy-Weisbach e, etc.

You need to pick the head loss equation that you like and account for roughness with the appropriate changes in coefficients.

Thanks for your reply, I think i was not able to put my question properly.

If i i do roughness adjustment here(red bounded area), what will be change in value of C

That particular roughness adjust is something you can use when for example you know that cast iron pipe laid before 1920 has a C-factor of 40. You would create a selection set containing all of those pipes. Once you open the adjustments manager by clicking the ellipse button, you would set that selection name to Scope, the Operations to Set and the Value to 40. Then all of those pipes would have a C-factor of 40.

This is useful for a quick sensitivity analysis but I usually prefer to change things in a new scenario.