COMPRESSIBLE STEADY FLUID FLOW
Consider air flow in a converging channel with an inlet area of 60 cm^2 and an exit area of 40 cm^2. At the inlet, the average velocity is 100 m/s, the pressure is 150 kPa, and the temperature is 300 K. [See schematic below. Note we assume adiabatic flow.] The velocity at the exit is 250 m/s. [We will need to find the exit pressure and the temperature.]
The surrounding atmospheric pressure is 101 kPa. Treat air as an ideal gas, so that the density = p/RT, and the enthalpy, h = cpT. [Recall for air, R = 0.287 kJ/kgK and assume cp = 1.00 kJ/kgK.]
PROBLEM: Using conservation of mass, energy, and momentum, show all work and calculate:
(a) Mass flow rate through the channel (kg/s)
(b) The exit pressure (kPa)
(c) The exit temperature (K)
(d) The net force, F, required to keep the channel in place (kN)
101 kPa
A = 60 cm^2, V = 100 m/s, P = 150 kPa, T = 300 K
A = 40 cm^2, V = 150 m/s, P = ?
Open system
