A converging-diverging nozzle is used to accelerate water at the state of superheated steam. The process in the nozzle is adiabatic, b/c it occurs very rapidly (order of a few seconds if not milliseconds). At the entrance of the nozzle, the pressure is p, = 20 MPa, the temperature is T, = 700 °C and the velocity of the steam is u̟ = 50 m/s. At the exit, the pressure is p, = 4 MPa, the velocity of the steam is uz = 1092.5475 m/s and the cross sectional area is Az = 0.01 m². The mass flow rate is defined as ṁ = pu A , with p the density of the fluid. Determine :
(A) determine the state of the stream as well as its temperature at the exit of the nozzle
(B) the mass flow rate
(C) the cross-sectional area at the inlet
(D) the mach number at the exit. Is the flow compressible
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There is no change with time so the process is in a steady state. The heat transfer is negligible as the system is adiabatic in nature. The temperature at the exit is obtained from steam tables. The mass flow rate is obtained from density, velocity, and area. The continuity equation is applied which states that the product of area and velocity are equal at points one and two. Mach number is the ratio of velocity and speed of the sound. This is a dimensionless number.
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