QUESTION $3$

Air flows through a pipe at a rate of $200\frac{L}{s}.$ The pipe consists of two sections of diameters $20$ cm and $10$ cm with a smooth reducing section that connects them. The pressure difference between the two pipe sections is measured by a water manometer. Neglecting frictional effects, if the inlet temperature of air is at $25C,$ due to the compression of the air at neck of the pipe contraction, the outlet temperature is measured at $30C,$ determine the differential height of water between the two pipe sections. Take the air density at $25C$ and $35C$ as $1\mathrm{.}20k\frac{g}{m^3}$ and $1\mathrm{.}19k\frac{g}{m^3}$ respectively.

$(10$ marks$)$