"In our initial analysis, we assume the curved region at the apex of the fountain is small enough, and has tight enough curvature, that the centripetal acceleration is much larger than the gravitational acceleration (v2/r≫g). The centripetal acceleration is then provided by the tension in the chain. If the (local) radius of curvature is r and the tension in the curved region is Tc" Also the lambda is mass per unit length
Why is Tc divided by r in the left half of the equation? If it was force per unit length then I would expect Tc to be divided by (pi)r instead of just r.