Question

3. (15 marks) As shown in the figure, a chamber has two pipe inlets (indicated using 1 and 2) and a nozzle outlet (indicated using 3). Helium gas flows through the system, and can be treated as an ideal gas with constant specific heats. The pressure of the helium at the two inlets and outlet is P, = 10 MPa, P2-15 MPa and P3-8 MPa, and the corresponding velocity of the helium gas is V - 10 m/s, V,- 15 m/s and V 300 m/s, respectively. The temperatures of the helium at the two inlets are identical, i.e. Ti- T2- 100 °C. The inner diameters of the inlet pipes are Di 200 mm and D2-150 mm. The system is well-insulated such that there is no heat transfer between the helium and the environment. (a) Determine the specific volume of the helium at inlets 1 and 2, vi and v2, in m'/kg. (3 marks) (b) Determine the mass flow rates at inlets 1 and 2, m, and m2, in kg/s. (3 marks) (c) Determine the temperature of the helium at the exit of the nozzle, T3, in °C. (7 marks) (d) Determine the inner diameter of the nozzle outlet, D3, in mm. (2 marks) P,-10 MPa, T,-100 "C D-200 mm . ?-10 m/s D3-?,VI 300 m/s P,-15 MPa, T,-100 °C- D2-150 mm, V2-15 m/s Figure for Problem 3

Answer 1

309X (33+100) o Xin 3KPa 1 m 2 ー22 2 2.osis4 9.1876 g (A

mix mx 72 2 0 09683S m3 18ブ6 X 0.096 ASS 888 m3/s D2 0.0 6144 m