Lecture T10: Review of Steady Flow Energy Equation and Stagnation Quantities

I reviewed the material we discussed in the last two lectures starting with the steady flow energy equation. This is a form of the first law written for an open system (with the same mass flow coming in and out). The only assumption I invoked was that I neglected changes in potential energy. That got me to and . The common difficulty with these two equations is understanding the physical difference between flow work (p2v2-p1v1) and shaft (or other external) work.

We then looked at the special case of an adiabatic process with no external work (q=0 and ws=0). This is an excellent model for the acceleration or deceleration of many fluids. For this case the stagnation enthalpy of the flow (hsubT = cpTsubT for an ideal gas) is a constant. If the flow is accelerated (c increasing), the enthalpy decreases (and the internal energy and the temperature). And vice versa if the flow is decelerated. If we deecelerate the flow to zero speed (c=0) then the temperature = the stagnation temperature and the enthalpy = the stagnation enthalpy. We also noted that if the process was also quasi-static, then pv^g=constant and we can define a stagnation pressure as the pressure one would reach if the flow were decelerated to zero speed in a particular reference frame via an adiabatic, quasi-static process with no external work. The stagnation quantities are dependent on the speed of the reference frame in which we assume the flow is stagnating ( a faster moving vehicle has a higher skin temperature). Also note that you can only apply the steady flow energy equation in a reference frame that is STEADY. So you must put yourself on the moving blade or on the moving aircraft (so you have a steady flow coming towards you), then determine what the speed of the flow is that is moving towards you, allow all of this kinetic energy (c^2/2) to be converted to enthapy (cpT) via an adiabatic process with no external work , arriving at the stagnation enthalpy (=cpTsubT for an ideal gas).(Add quasi-static as a requirement for the process if you want to determine the stagnation pressure).

We reviewed the PRS question we ended the last lecture with, and introduced one new PRS question.

Responses to 'Muddiest Part of the Lecture Cards'

(20 respondents out of 66 students)

1)Unclear on the frame dependence of stagnation temperature and related questions. (16 students) All of the mud cards focused on the same thing. So I will make a few general comments rather than answering each separately. First, we will have more time to go over this in the recitation on Tuesday. Also, you will have practice on the homework.