Problem

A 6-m-tall chimney shown in Fig. P14-92 is to be designed to discharge hot gases from a fi...

A 6-m-tall chimney shown in Fig. P14-92 is to be designed to discharge hot gases from a fireplace at 180°C at a constant rate of 0.15 m³/s when the atmospheric air temperature is 20°C. Assuming no heat transfer from the chimney and taking the chimney entrance loss coefficient to be 1.5 and the friction coefficient of the chimney to be 0.020, determine the chimney diameter that would discharge the hot gases at the desired rate. Note that P₃ = P₄ = P_atm and P₂ = P₁ = P_atm + ρ_{atm air} gh, and assume the hot gases in the entire chimney are at 180°C.