A cast iron pipe $(L=400m,D=150mm)$ is carrying $0\mathrm{.}05\frac{m^3}{s}$ of water at $15C.$ Compute the discharge if the difference in piezometric head is $20m.$ Assume the minor loss coefficients amount to $K=2\mathrm{.}5$ and $f=0\mathrm{.}025($justify value using Moody's diagram$).$