The steady flow energy equation (SFEE) is a thermodynamic relationship used to analyse open systems where fluid flows continuously under steady conditions. It relates heat transfer, work and changes in fluid energy including enthalpy, velocity and elevation.
Under steady flow conditions, mass flow rate and energy transfer remain constant with time. The equation is widely used in engineering applications such as turbines, compressors, nozzles and heat exchangers to evaluate energy changes within a control volume.
The steady flow energy equation (SFEE) is a form of the first law of thermodynamics applied to open systems where mass flows continuously through a control volume. It accounts for energy transfer due to heat, work, and fluid properties such as enthalpy, velocity and elevation.
The equation is widely used in engineering analysis of turbines, compressors, pumps, boilers, condensers and nozzles where steady operating conditions apply.
The steady flow energy equation relates to open systems working under steady conditions i.e in which conditions do not change with
time.
The boundary encloses a system through which fluid flows at a constant rate, whilst heat transfer occurs
and external work is done all under steady conditions ,that is , the rates of mass flow
and energy flow are constant with respect to time.
The equation for steady flow ( the steady flow energy equation ) is generally written per unit mass as
General form per unit mass:
q - w = (h2 - h1) + (v22 - v12)/2 + g(z2 - z1)
q = heat transfer across boundary per unit mass
w = external work done by system per unit mass
z = fluid height
v = fluid velocity
h = fluid enthalpy ( u (internal energy + pv (pressure.specific volume)
Note in the examples below the system control volumes are defined by the red dashed line.
Potential energy (z) assumed to be constant..
Kinetic energy changes (1 to 2) assumed to be very small
Heater
w = 0 therefore
q = h2-h1
Potential energy (z) assumed to be constant..
Kinetic energy changes (1 to 2) assumed to be very small
Turbine
q = 0 therefore
w = h2-h1
Potential energy (z) assumed to be constant..
The higher velocity at orifice section is dissipated in tube downstream of the orifice and
therefore the kinetic energies at 1 and 2 are similar
q = w = 0 therefore
therefore h1 = h2
Potential energy (z) assumed to be constant..
Kinetic energy changes are assumed to be significant
Nozzle
q = w = 0 therefore
(v22 - v12 ) /2 = (h1 - h2 )
The steady flow energy equation is used when analysing systems where fluid flows continuously and properties do not change with time. Typical applications include turbines, compressors, heat exchangers, nozzles and pipe flow systems.
The steady flow energy equation is a fundamental tool in thermodynamic system design and analysis. It is used to determine heat transfer, work output and energy changes in a wide range of engineering systems.
In turbines, it is used to calculate work output based on enthalpy drop. In compressors and pumps, it determines the work required to increase pressure. In nozzles, it is used to calculate velocity changes from pressure and enthalpy differences.
The equation is also applied in the design of heat exchangers, boilers and condensers where energy transfer between fluids is critical.
Summary: The steady flow energy equation relates heat transfer, work and changes in fluid energy for open systems operating under steady conditions. It is widely used in the analysis of turbines, compressors, nozzles and heat exchangers.
The steady flow energy equation (SFEE) is a thermodynamic relationship used to analyse open systems where fluid flows continuously. It relates heat transfer, work and changes in fluid energy such as enthalpy, velocity and elevation.
The general form of the steady flow energy equation per unit mass is: q - w = (h₂ - h₁) + (v₂² - v₁²)/2 + g(z₂ - z₁), where q is heat transfer, w is work done, h is enthalpy, v is velocity and z is elevation.
The equation is used for systems operating under steady conditions where mass and energy flow rates remain constant. It is commonly applied to turbines, compressors, nozzles, pumps and heat exchangers.
The main assumptions are steady-state operation, constant mass flow rate, and that properties do not change with time. In many cases, changes in kinetic and potential energy may also be neglected.
For turbines, the steady flow energy equation is often simplified by assuming no heat transfer and negligible kinetic and potential energy changes, resulting in work output being equal to the enthalpy drop.
In nozzles, the equation is used to calculate velocity changes. Heat transfer and work are often assumed zero, so the decrease in enthalpy is converted into an increase in fluid velocity.