4.1.5. Pressure, Streamlines and Streaklines

4.1.5.1. What are the components of pressure?

  • Static/thermodynamic - expresses a fluid’s temperature or internal energy, e.g. from ideal gas law \(\longrightarrow\) \(p_{static}=nk_bT\)
  • Hydrostatic - expresses a fluid’s depth \(\longrightarrow\) \(p_{hydrostatic}=\rho gh\)
  • Dynamic - expresses a fluid’s velocity \(\longrightarrow\) \(p_{dynamic}={1 \over 2} \rho u^2\)
  • Stagnation - the pressure that would be reached if flow is brought to rest frictionlessly \(\longrightarrow\) \(p_{stagnation} = p_{static} + p_{dynamic}\)
  • Total - sum of all components of pressure \(\longrightarrow\) \(p_{total} = p_{static} + p_{dynamic} + p_{hydrostatic}\)

4.1.5.2. What is the definition of pressure?

  • Normal force per unit surface

  • Measured as:
    • Absolute (relative to vacuum)
    • Relative (relative to atmosphere)
  • The relationship between relative and absolute pressure is: \(p_{rel} = p_{abs} - p_{atm}\)

4.1.5.3. What is a streamline?

  • A curve that is instantaneously tangent to the velocity field throughout the flow field.
  • In unsteady flow this changes with time.
  • Usually generated computationally.

4.1.5.4. What is a pathline?

  • The trajectory of a fluid particle of fixed identity over a period of time.
  • In unsteady flow pathlines cannot change their time history
  • Usually generated experimentally.