Continuity Equation Explained | Steam Turbine Example | Thermodynamics

Welcome to Engineering Hack! In today's video we are introducing the continuity equation by bringing a simple turbine problem. The idea behind the continuity equation is that you have a mass flow entering a system that is equal to the mass flow leaving the system, regardless of how many entrances and exists a system has. It is a very intuitive concept and it can be applied in a variety of real world scenarios (e.g. gas power plant). As important as understanding how to use the continuity equation is to understand when not to use it. If you have mass accumulation in your system (or in your control volume), then the continuity equation cannot be used, and a different approach is required. Other than that, we need to know how to read the steam tables to define the states, so if you are not sure how to do that yet, jump into the previous videos.

Problem statement: A steam turbine receives 5 m³/s of water vapor at 3 MPa and 600 °C. The turbine has an intermediate phase were steam is extracted. The temperature and pressure of the steam in the extraction pipe are equal to 200 °C and 600 kPa. The pressure and the quality in the main discharge pipe of the turbine are equal to 20 kPa and 90%, respectively. Knowing that the mass flow in the extraction pipe is equal to 15% that of the incoming vapor and that the speed in the main discharge pipe is 20 m/s, determine the volumetric flow in the extraction pipe and the diameter of the main turbine discharge.

Answer:
Vol 2 = 2 m³/s
Diameter 3 = 3.75 m

To learn more please watch the video till end and if you have a question just ask in the comments section.
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[DeathrashWhiplash]

This is a very helpful video. What books did you use to learn thermo? I studied Reed's heat for marine engineers. Thanks