Lecture P2: Integral Momentum Equation

In this lecture we started with a review of the material discussed last lecture via a concept question (Q1). This was intended to reinforce that that thrust is primarily a balance between momentum flux into an engine and momentum flux out of an engine. We then discussed the integral momentum equation for a fixed mass in a reference frame which is accelerating relative to an inertial reference frame. The equation is identical to that used in fluids with the addition of a term to account for the acceleration of the reference frame (which you have seen in Dynamics before). We then discussed in some detail the calculation of momentum flux using the integral momentum equation. Please review the concept question (Q2). It is important that you understand how to apply this. Note that there was some concern expressed about the sign obtained in this example. Since I specified that you were to find the momentum flux into the surface, then the sign should be positive (since the flow is clearly into the surface). But to avoid confusion, I just changed the wording of the problem to say "determine the momentum flux across the surface". Thus, if the calculation results in a minus sign, then the flow is opposite to the outward normal (i.e. into the surface); if the calculation results in a positive sign the flow is out of the surface.

Responses to 'Muddiest Part of the Lecture Cards'

(4 respondents--must be the last lecture before spring break)

1) So what if we want the total momentum flux for this problem? (1 student) The total momentum flux is just the magnitude of the vector composed of the x, y, and z components.

2) Donuts = more attentive students (1 student). I'm on it.

3) No mud (2 students). Good.