Bobad, I am not sure that wire bending trick is very accurate.
If the stream were broad but very shallow you would overestimate
the cross sectional area a lot if you deformed the wire into a square or a squarish rectangle. For example, take a skinny rectangle (1/2 ft x 5 1/2 ft) with a circumference of 12 ft and an area of 2 3/4 sq ft. You can deform this 12 ft "wire" loop into a 2ft x 4ft rectangle with an area of 8 sq ft. The skinnier the rectangle, the smaller the area, given the same circumference.