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f13_mud

# f13_mud - Lecture F13 Mud Bernoulli Equation(25 respondents...

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Lecture F13 Mud: Bernoulli Equation (25 respondents) 1. How is ρu du/dx = 1 2 ρ d ( u 2 ) /dx ? (2 students) You can see this easily just by differentiating d ( u 2 ) /dx via the product rule. 2. How is ρu du = 1 2 ρ d ( u 2 ) ? (2 students) Take the differential d ( u 2 ) using the product rule. This is essentially the same operation as in mud 1 above. 3. How did you go from 1 2 ρ d ( u 2 ) /dx + dp/dx = 0 to 1 2 ρ u 2 + p = C ? (1 student) Via an indefinite integration in x : integraldisplay parenleftbigg 1 2 ρ d ( u 2 ) /dx + dp/dx = 0 parenrightbigg dx 4. How did you know you can multiply x -momentum by dx ? (1 student) You can always multiply equations by anything you want, whether it’s useful or not to do so. Bernoulli in the 1700’s figured out that multiplying by dx actually gets you somewhere. 5. What form of vector V should you use in Bernoulli? φ ? (1 student) In aerodynamic flows, the velocity used in Bernoulli is usually defined via φ ( x, y, z ). There are exceptions, however, such as when a pitot probe is used inside a boundary

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f13_mud - Lecture F13 Mud Bernoulli Equation(25 respondents...

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