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Section
4: Inviscid Flow I: Euler's Equation of Motion, Bernoulli's Integral, and
the Effects of Streamline Curvature |
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4.1 |
Euler's
equation for inviscid motion: a relationship between fluid acceleration
(convective and temporal) and pressure distribution. |
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4.2 |
Concepts
for describing fluid flows: streamlines, particle paths, and streaklines. |
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4.3 |
Euler's
equation for steady flow expressed in streamline coordinates: the pressure-velocity
relation along the streamline direction, and the pressure gradient normal
to streamlines when streamlines have curvature. Comments on the "inviscid"
flow approximation and the boundary conditions that are appropriate for
velocity and pressure in such flows. |
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4.4 |
Incompressible
flow examples involving both Bernoulli's integral and the effects of streamline
curvature. Classroom demonstrations of the Bernoulli effect and the streamline
curvature effect (the latter being the origin of lift on airfoils). |
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4.5 |
Bernoulli's
integral for two types of steady, isentropic, compressible flows: (a) perfect gases and (b) liquids with
constant compressibility. Isentropic
expansion of a gas into a vacuum. A criterion for "incompressible flow. |
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4.6 |
The
general form of Bernoulli's integral for unsteady flow. Examples: startup problems, Rayleigh bubble
oscillations, etc., mainly for incompressible flows. |
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4.7 |
Introductory
comments on potential (vorticity-free) flow and the velocity potential f. Incompressible
flows as solutions of Ñ2f = 0 with ∂f/∂n =0 at solid
boundaries. The equation for
pressure in terms of the velocity potential f |
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Reading
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Fay, Chapter
4 |
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Problem Set Section 4
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Problem 4.1 |
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Problem 4.4 |
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Problem 4.8 |
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Problem 4.9 |
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Problem 4.15 |
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Problem 4.18 |
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Problem 4.19 |
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Problem 4.21 |
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Problem 4.23 |
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Problem 4.24 |
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Problem 4.28 |
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