What is the steady flow energy equation (SFEE)?

Short Answer:

The Steady Flow Energy Equation (SFEE) is a form of the First Law of Thermodynamics applied to systems where mass and energy enter and leave continuously, such as turbines, compressors, nozzles, and heat exchangers. It helps in analyzing energy balance in steady-flow devices by relating heat, work, and energy forms like pressure, velocity, and height.

In a steady-flow system, the SFEE explains how the energy entering and leaving a control volume stays balanced. It considers internal energy, kinetic energy, potential energy, shaft work, and heat transfer. SFEE is very useful in designing and analyzing thermal and fluid flow machines.

Detailed Explanation:

Steady flow energy equation

In thermodynamics, the Steady Flow Energy Equation (SFEE) is used to understand how energy flows in and out of a system where mass enters and exits continuously, and the conditions at every point remain constant over time. These systems are called steady-flow systems. SFEE is a special case of the First Law of Thermodynamics applied to open systems, also known as control volumes.

This equation is especially useful in analyzing devices that operate continuously like turbines, compressors, pumps, boilers, nozzles, diffusers, and heat exchangers. In all these devices, energy enters and leaves with the flow of mass, and SFEE helps in tracking that energy balance.

Basic Assumptions of SFEE

Before applying the SFEE, the following assumptions are generally made:

  1. The process is steady, meaning all properties remain constant with time.
  2. Mass flow rate entering and leaving is equal.
  3. Heat and work interactions are included.
  4. The fluid behaves as a continuous substance (not molecular level).
  5. Properties at entry and exit sections are known or can be calculated.

General Form of SFEE

The general form of the steady flow energy equation is:

Q̇ – Ẇ = ṁ[(h₂ – h₁) + (V₂² – V₁²)/2 + g(Z₂ – Z₁)]

Where:

  • Q̇ = Heat transfer rate into the system (kJ/s)
  • Ẇ = Work done by the system (shaft work, kJ/s)
  • ṁ = Mass flow rate (kg/s)
  • h = Specific enthalpy (kJ/kg)
  • V = Velocity of fluid (m/s)
  • Z = Height or elevation (m)
  • g = Acceleration due to gravity (9.81 m/s²)

This equation says that the net energy entering (through heat and work) is equal to the change in total energy of the fluid which includes:

  • Enthalpy (internal energy + flow work)
  • Kinetic energy (due to velocity)
  • Potential energy (due to elevation)

Physical Meaning of Each Term

  1. Heat Transfer (Q̇):
    Heat added or removed during the process.
  2. Work Transfer (Ẇ):
    Work done by the system (like shaft work in turbines or work required in compressors).
  3. Change in Enthalpy (h₂ – h₁):
    Shows the energy change due to pressure and temperature differences.
  4. Change in Kinetic Energy [(V₂² – V₁²)/2]:
    Represents the increase or decrease in velocity of the fluid.
  5. Change in Potential Energy [g(Z₂ – Z₁)]:
    Energy change due to height difference in the fluid flow.

Applications of SFEE

SFEE is used in the analysis of many engineering devices:

  • Turbines: Convert enthalpy of steam or gas into work.
  • Compressors and Pumps: Require work input to increase pressure.
  • Boilers and Heat Exchangers: Involve heat addition or removal at steady flow.
  • Nozzles and Diffusers: Where velocity and pressure change significantly.
  • Jet Engines: Where both velocity and enthalpy change during flow.

By using SFEE, engineers can calculate the required or produced work, needed heat supply, and flow energy change in these devices.

Simplified Forms of SFEE

Depending on the device, some terms can be neglected:

  • For nozzles: Ẇ = 0, Q̇ = 0, and Z difference is small
  • For turbines: Q̇ ≈ 0, Z and V changes are sometimes ignored
  • For heat exchangers: Ẇ = 0, Z and V changes negligible

These simplifications make the SFEE easier to solve in practical cases.

Conclusion

The Steady Flow Energy Equation (SFEE) is a key thermodynamic tool used to analyze energy flow in systems where mass enters and exits continuously under steady conditions. It balances heat, work, and all forms of energy (enthalpy, kinetic, and potential) for control volume systems like turbines, pumps, and nozzles. SFEE is very important in mechanical engineering to design energy-efficient thermal and fluid systems.