The formula for calculating the bent section of the hose length around a radius is derived from the basic formula that the circumference of a circle = 2πR, where R = the radius of the circle, and π = a constant, = 3.142.
So, if the hose goes around a 90˚ bend, which is 1/4 of a full circumference, and the radius of the bend is R, then the length of the hose around the bend is = 1/4 x 2πR. Or half way round, in a U-shape, = 1/2 x 2πR.
Note: In calculating the length of a hose assembly, the (non-flexible) length of the end fittings must be added in, also the length of any straight sections of hose, as in the following example:
To calculate the length for a 2” bore size hose with flange end fittings, to be fitted in a 90˚ configuration with one leg 400mm long, the other 600mm long.
Length of Bent Section (yellow) = 1/4 x 2πR (334) = 1/4 x 2 x 3.142 x 334 = 525mm
Length of top, Straight Section, including the top end fitting length = 600 - 334 = 266mm
Length of bottom end fitting = 66mm
Total length of Hose Assembly = 525 + 266 + 66 = 857mm
Things to consider
If in doubt, consult Aflex Hose.