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Unformatted text preview: Lecture F12 Mud: Stream Function, Potential Function (25 respondents) ¯ ¯ 1. The book claims “ 2 = 1 represents mass ﬂow perpendicular to the page”. Isn’t 2-D ﬂow in the plane of the page? (1 student) It actually says “mass ﬂow per unit depth perpendicular to the page”. The “perpen- dicular” refers to the unit depth, not to the ﬂow. ¯ 2. What’s the difference between and ? (2 students) ¯ is the most general type of stream function, and gives the mass ﬂux components: ¯ ¯ / y = u − / x = v For low speed ﬂows where is a constant, it is convenient to absorb the constant ¯ factor into the stream function by defining = / . We now have: / y = u − / x = v ¯ It’s important to remember that can be used only for low speed ﬂows, while has no such restriction. ¯ ¯ The difference 2 − 1 gives the mass ﬂow between two streamlines, while 2 − 1 gives the volume ﬂow between two streamlines (but only in low-speed ﬂow)....
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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