Assume that an air tank at T₁ = 27 °C and P₁ = 2 atm discharges into the atmosphere through a steel pipe of diameter D = 2.5 cm. The tank is large enough that T₁ and P₁ remain nearly constant. The ambient temperature is also 27 °C.

(a) If the flow were isothermal, what pipe length L_c would just suffice to create choking? What then would be the mass flow rate w?

(b) If the flow were isothermal, what would w be if L = 0.5L_c?

(c) Repeat part (a) for adiabatic flow. Note that the gas exiting the pipe will now be cooler than 27 °C. Thus, the Reynolds numbers based on the inlet and outlet conditions will differ. However, show that the corresponding friction factors are nearly equal to one another and to the isothermal f.]