Hi JohnM77,

If you draw the radii from the circle centre to the left and right edges of the surface of the water in your diagram, draw the radius from the centre to the bottom of the pipe, you have 2 back-to-back right-angled triangles sitting on the water with top apex at the pipe centre.

Label the angle at the centre for either triangle A.

Then you work it through as the triangle heights are r-H.

The cross-sectional area of the water equals the (sector area)-(the sum of the triangle areas)

where