Basic Equations for One-Dimensional Flow

• 
  Here we will study a class of compressible flows that can be treated as one dimensional flow. Such a simplification is meaningful for flow through ducts where the centreline of the ducts does not have a large curvature and the cross-section of the ducts does not vary abruptly.
  
• In one dimension, the flow can be studied by ignoring the variation of velocity and other properties across the normal direction of the flow. However, these distributions are taken care of by assigning an average value over the cross-section (Fig. 39.3). 
  
• The area of the duct is taken as A(x) and the flow properties are taken as p(x), ρ(x), V(x) etc. The forms of the basic equations in a one-dimensional compressible flow are;
  

  • Continuity Equation
  • Energy Equation
  • Bernoulli and Euler Equations
  • Momentum Principle for a Control Volume

Fig 39.3 One-Dimensional Approximation