a) Steady, frictionless air, at 100 kPa and 25 C, flows in a horizontal duct that has a cross sectional flow area reduction in it. The reducer smoothly forms the 18 cm diameter duct to a 10 cm duct. A U-tube water manometer connects on both ends of the reducer component and shows a liquid difference level of h = 8 cm. The flow in the larger 18 cm duct is considered to be moving very slowly compared to the 10 cm duct flow. Adapt Bernoulli's and ideal gas equations to determine the flow's velocity in the smaller duct. (b) Note that the velocity is proportional to the square root of the manometer reading {i.e. V=k*h^0.5}where k is a proportionality constant. And uncertainty is the differential of the velocity divided by the velocity {dV/V} Determine the uncertainty of the velocity measured when the uncertainty of the manometer reading is +/- 2mm. R = 0.287 kPa*m^3 / kg*K water density = 1000 kg/m3