Solution:

Using energy Eq$.$ for steady state $($initial state$),$

$15+h_p=\frac{V_2^2}{2g}+\frac{f_1{L}_1}{D_1}\frac{V_1^2}{2g}+\frac{f_2{L}_2}{D_2}\frac{V_2^2}{2g}+0\mathrm{.}5\frac{V_1^2}{2g}$

$"1"$ and $"2"$ refer to the $25cm$ and $15cm$ diameter pipes.