First Law Applied to Steady Flow Process

Definition

The First Law of Thermodynamics, when applied to a steady flow process, represents the conservation of energy for an open system where mass enters and leaves at a constant rate. In a steady flow system, the properties of the fluid at any given point within the control volume do not change over time, and the mass flow rate remains constant throughout the process.

Main Content

1. Conservation of Mass (Continuity Equation)

• In a steady flow process, the mass entering the system must equal the mass leaving the system per unit time.
• Mathematically, this is expressed as $\dot{m}_1 = \dot{m}_2 = \dot{m}$, where $\dot{m}$ is the mass flow rate ($\rho A v$).

2. Energy Balance Equation

• The energy entering the control volume (via mass, heat, and work) must equal the energy leaving it, plus any energy stored or transformed.
• The steady-flow energy equation (SFEE) is: $\dot{m} (h_1 + \frac{v_1^2}{2} + gz_1) + \dot{Q} = \dot{m} (h_2 + \frac{v_2^2}{2} + gz_2) + \dot{W}$

3. Energy Terms Explained

• Enthalpy ($h$): Represents the total energy content of the fluid, combining internal energy and flow work ($u + pv$).
• Kinetic and Potential Energy: These account for the velocity ($v^2/2$) and elevation ($gz$) changes as the fluid moves through the device.

Working / Process

1. Defining the Control Volume

• Identify the boundary of the device (such as a turbine, nozzle, or pump) through which the fluid flows.
• Ensure the control surface is fixed in space so that the mass flow rates at the inlet and exit remain constant over time.

2. Setting Steady State Assumptions

• Assume that the properties (pressure, temperature, velocity) at the inlet and exit do not change with time.
• Verify that the rate of work done ($\dot{W}$) and heat transfer ($\dot{Q}$) are consistent values.

3. Applying the Energy Equation

• Substitute the known values of mass flow, heat transfer, and mechanical work into the SFEE.
• Solve for the unknown variable, such as the power output of a turbine or the heat loss from a heat exchanger.

       Mass In (m1)           Mass Out (m2)
      -------------> [ Device ] ------------->
       Properties (1)  (CV)    Properties (2)
      -------------> [      ] ------------->
          Heat (Q)           Work (W)

Representation of a Steady Flow Control Volume (CV)

Advantages / Applications

• Turbines: Used in power plants to convert the enthalpy of high-pressure steam or gas into mechanical work.
• Nozzles and Diffusers: Essential in aerospace engineering to accelerate or decelerate fluid streams by changing pressure into kinetic energy.
• Compressors and Pumps: Utilized in industrial cooling and fluid transport systems to increase the pressure of gases or liquids.

Summary

• The steady flow process is a fundamental analysis tool where mass and energy entering the control volume are balanced by what leaves.
• It assumes time-independent conditions, meaning pressure, density, and velocity at any cross-section remain constant.
• The core of the analysis is the Steady Flow Energy Equation (SFEE), which accounts for heat, work, enthalpy, kinetic energy, and potential energy.
• Important terms: Steady Flow Energy Equation (SFEE), Mass flow rate, Control Volume, Enthalpy, and Steady State.