This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: vector Lecture F10 Mud: Momentum Theorem Applications (37 respondents) 1. Whats the difference between D () /Dt and d () /dt ? (1 student) What were after is the time rate of change of some owfield quantity like p ( x, y, z, t ), as seen by a sensor moving as a uid element. Just writing dp/dt is very sloppy math, since p depends on four variables x, y, z, t , not just on t . So we must work with the four partial derivatives of p . The correct expression for the time rate of change seen by the sensor is p p p p + u + v + w t x y z but this is long and tedious to write. So we use the shorthand Dp/Dt for this whole expression. 2. Not clear how D/Dt differs from /t . (2 students) The partial derivative /t merely gives the rate of change of density seen by fixed sensor sitting at one particular x, y, z location. But were after the rate seen by a sensor which moves with the ow velocity, so the sensors x, y, z are continually changing. Using the chain rule then brings in the three spatial partial derivatives /x, y, z whose contributions are added to the /t term. See point 1 above....
View
Full
Document
This note was uploaded on 01/28/2012 for the course AERO 16.01 taught by Professor Markdrela during the Fall '05 term at MIT.
 Fall '05
 MarkDrela

Click to edit the document details