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.
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?