I've a question concerning the use of the Bernoulli principle. Let's say I have a pipe filled with air at atmospheric pressure, with a constricting section ala the figure below. The volume before the throat is known.

enter image description here

The flow is static - it is not moving at time t = 0. At t > 0 a gas with known gamma starts flowing into Area 1, at some mass flow rate m_dot. How would you determine the time dependent velocity at the throat?

  • $\begingroup$ Use Energy Equation as well as Continuity Equation. $\endgroup$
    – Benjamin
    Mar 20, 2016 at 0:07
  • $\begingroup$ Bernoulli's equation is only going to give you a steady state solution. To solve transient, dynamic behavior you have to use the Navier Stokes equations for compressible flow and carefully define the boundary conditions. You would require computational methods to do this. $\endgroup$
    – docscience
    Mar 20, 2016 at 15:41
  • $\begingroup$ @docscience Thank you! I've been looking for a new angle on the issue, this seems to do something new. Thanks for the input $\endgroup$
    – eow
    Mar 20, 2016 at 17:31


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