Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering Summary of Energy Topics Chapter 1: Thermodynamics / Energy Introduction Chapter 2: Systems & Processes Chapter 3: Work, Energy, Temperature & Heat Chapter 4: Work Processes of Closed Systems Chapter 5: Thermodynamic Properties Chapter 6: Steam Tables Chapter 7: Ideal Gases Chapter 8: Conservation of Mass & Energy Chapter 9: 1 st Law of Thermodynamics Chapter 10: Steady Flow Energy Equation Chapter 11: Combustion & Refrigeration Chapter 12: 2 nd Law of Thermodynamics Chapter 13: Entropy Chapter 14: General Energy

Chapter 10: Steady Flow Energy Equation Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering

STEADY FLOW ENERGY EQUATION This derivation assumes: -An adiabatic system, Q = 0 -No friction or work done in moving through the system, W=0 -The datum point is zero gravity z=g -Volume doesn’t change V 1 =V 2 - No change in internal energy, u 2 =u 1 An alternative form, excluding many of these assumptions is:. Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering Q is the rate of heating applied to the control volume W is the rate of work input (watts (Js-1)) m is the amount of mass/unit time Chapter 10: Steady Flow Energy Equation

Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering

Chapter 10: Steady Flow Energy Equation Dr. Joseph Stokes School of Mechanical & Manufacturing Engineering

Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering

Chapter 10: Steady Flow Energy Equation Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering CONSTANT PRESSURE HEATING OR COOLING PROCESS A device in which a fluid is heated or cooled in steady flow is often idealised as a system in which there is negligible pressure drop, the changes in kinetic and potential energy between entry and exit are negligible, and where no shear work is done on or by the system. Examples include: a boiler (liquid water enters and steam leaves in steady flow), a condenser (vapour enters and condensed liquid leaves), or either side of a liquid-to-liquid heat exchanger, (liquid is heated or cooled from one temperature to another).

Chapter 10: Steady Flow Energy Equation Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering

Chapter 10: Steady Flow Energy Equation Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering THE ADIABATIC WORK PROCESS Pumps, turbines, fans, and compressors can be described as steady flow devices as the heat transfer is negligible and changes in the potential energy and kinetic energy between entry and exit are negligible. The steady flow equation reduces to the form: W 2 1

Chapter 10: Steady Flow Energy Equation ADIABATIC THROTTLING PROCESS A process in which a flow restriction such as a porous plug or a partially open valve causes a pressure drop is known as a throttling process. As this occurs within a small volume, heat transfer is usually negligible, no shear work is done on or by the system: so that is the enthalpy downstream of the throttle is equal to that upstream.

Chapter 10: Steady Flow Energy Equation Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering EXAMPLE 10.2 A throttle valve allows steam with a dryness fraction of 0.97 to pass through it, where its pressure is reduced from 2.0MPa to 0.1MPa. Determine the temperature of the steam before and after the valve?

Chapter 10: Steady Flow Energy Equation Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering EXAMPLE 10.2 A throttle valve allows steam with a dryness fraction of 0.97 to pass through it, where its pressure is reduced from 2.0MPa to 0.1MPa. Determine the temperature of the steam before and after the valve?

Chapter 10: Steady Flow Energy Equation Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering EXAMPLE 10.2 A throttle valve allows steam with a dryness fraction of 0.97 to pass through it, where its pressure is reduced from 2.0MPa to 0.1MPa. Determine the temperature of the steam before and after the valve?

Chapter 10: Steady Flow Energy Equation Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering AN ADIABATIC NOZZLE

Chapter 10: Steady Flow Energy Equation Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering EXAMPLE 10.3 A system for the analysis of the flow between two adjacent stationary blades within a turbine allows air to enter normal to its surface at position 1 and leaves normal to its surface at position 2. There is no flow across any other part of the boundary. The air at position 1 has a pressure of 0.48MPa, a temperature of 360°C, and has negligible velocity. It undergoes an adiabatic equilibrium process within the blade passage flow system and leaves at position 2 with a pressure of 0.41MPa. Calculate the exit temperature and the exit velocity of the air. (  Air = 1.4; c p =1.005 x 10 3 ) 1 2

Chapter 10: Steady Flow Energy Equation Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering EXAMPLE 10.3 A system for the analysis of the flow between two adjacent stationary blades within a turbine allows air to enter normal to its surface at position 1 and leaves normal to its surface at position 2. There is no flow across any other part of the boundary. The air at position 1 has a pressure of 0.48MPa, a temperature of 360°C, and has negligible velocity. It undergoes an adiabatic equilibrium process within the blade passage flow system and leaves at position 2 with a pressure of 0.41MPa. Calculate the exit temperature and the exit velocity of the air. (  Air = 1.4; c p =1.005 x 10 3 )

Chapter 10: Steady Flow Energy Equation STEADY FLOW ENERGY EQUATION Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering

Chapter 10: Steady Flow Energy Equation Dr. Owen Clarkin School of Mechanical & Manufacturing Engineering