Correct option is (a) hf = f* (L/(s *d)) * ((1-e) /e^3) * (v^2/g)

For explanation I would say: The expression of the Rose equation is given by hf = f* (L/(s *d)) * ((1-e^4) /e^3) * (v^2/g) where hf = head loss, d = diameter of pipe. L = length of pipe and v=approach velocity and f = 1.067CD, Where CD is the coefficient of drag.