Does anyone have a direct solution for this problem?

Consider a pipe of radius r, parially filled with water. The cross-sectional area of the water standing in the pipe is known. What is depth H of the water standing in the pipe?

I've been able to solve for H using an iterative method, but I have not found a direct solution formula. Does anyone have a formula to calculate H is r and the area of the shaded blue area are known?

Thanks,

John