Q$3-)$ Air flows upward at a specified rate through an inclined pipe whose diameter is reduced through a reducer. Calculate; a$-)$ the differential height between fluid levels of the two arms of a water manometer attached across the reducer, and b$-)$ pressure differences between cross$-$sections $1$ and $2$ seen in figure Q$3.$ Assumptions: The flow through the duct is steady, incompressible, and irrotational with negligible frictional effects $($so that the Bernoulli equation is applicable$).$ Air is an ideal gas, the effect of the air column on the pressure change is negligible because of its low density. The airflow is parallel to the entrance of each arm of the manometer, and thus no dynamic effects are involved. Properties: We take the density of water to be $=1000k\frac{g}{m^3}.$ The gas constant of air is $R=0\mathrm{.}287$kPa$*\frac{m^3}{k}g*K,{}_{\text{a}\text{i}\text{r}}=1\mathrm{.}19k\frac{g}{m^3},Q=0\mathrm{.}059\frac{m^3}{s},A_1=0\mathrm{.}06m^2,A_2=0\mathrm{.}04m^2,Z=0\mathrm{.}2m.$