An insulated mixing chamber receives 0.5 kg/s of steam at 3 MPa and 300°C through one inlet, and saturated liquid water at 3 MPa through the other inlet. The combined stream exits with a quality of 80% and a pressure of 3 MPa. A fan, using 10 kW of power, is used to aid the mixing process. Determine the mass flow rate of the saturated liquid stream entering the mixing chamber

Explanation:

The mixing chamber can be modelled by applying the First Law of Thermodynamics:

Since that mass flow rate of water at inlet 1 is the only known variable, the expression has to be simplified like this:

Besides, the following expression derived from the Principle of Mass Conservation is presented below:

Then, the expression is simplified afterwards:

Specific enthalpies are obtained from steam tables and described as follows:

State 1 (Superheated vapor)

State 2 (Saturated liquid)

State 3 (Liquid-Vapor mixture)

The ratio of the stream at state 2 to the stream at state 1 is:

The mass flow rate of the saturated liquid is:

answer:

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