$($a$)$ Water flows in a circular pipe. At one section the diameter is $0\mathrm{.}3m,$ the static pressure is $260$kPa gauge, the velocity is $3\frac{m}{s}$ and the elevation is $10m$ above ground level. The elevation at a section downstream is $0m$ and the pipe diameter is $0\mathrm{.}15m.$ Find the gauge pressure at the downstream section. The head losses due to friction between these sections equal to $30\%$ of the outlet velocity head. Assume density of water to be $999k\frac{g}{m^3}.(7$ marks$)$