Find R for two arcs joined tangentially

Question

I am trying to design a nozzle and require R to design it. I know the parameters as shown in the picture, with the two circles connecting tangentially, but am having a lot of trouble finding R.

I've tried to build triangles to relate the angle of the straight line connecting them (0.15+R line) but then I end up with two variables (theta and R) and only one equation based on the triangle with hypotenuse (0.15+R) and 0.25 as the base. Any tips on how to solve this?

Thanks!

Answer 1

It's not clear to me how this "nozzle" shape is defined, but from the diagram and the description^* of your "failed" attempt, it seems that the basic Pythagorean Theorem for right triangles suffices.

Namely, solve for $R$ from

$$(0.15+R)^2 = (0.25)^2 + (0.025+R)^2$$

Does this suit your needs?

^{*The fact that the hypotenuse (of length $0.15+R$) is one smooth straightline comes from the requirement that the two circular arcs share a tangent at the connecting point.}