I have a math question ?

consider looking at a cross section of pipe, with radius p.

From the centre of this circle mark the origin and x and y axes.

Let's assume you are going to but a hole with radius h into the pipe (h < p)

This will look like a vertical line on your diagram somewhere on the right hand side of the circle.

Now, the equation of this circle is x^2 + y^2 = p^2

But the hole will intersect at y = h and y = -h

so we have x^2 + h^2 = p^2 or x = sqrt(p^2 - h^2)

This 'x' will be the distance from origin of pipe to hole

So the distance you require will be:

p - x

or

p - sqrt(p^2 - h^2)

so for example if your pipe is radius 2 inches and hole radius 1.5 inches, the depth required will be

2 - sqrt(4 - 1.5^2) = 0.677 inches (3 dp)