VFF equations Flashcards
What is the material derivitave?
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Express the velocity gradient tensor in terms of the rate of strain tensor and the rate of rotation tensor.
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How does the rate of rotation tensor relate to the vorticity?
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What is the continuity equation (differential form) for compressible fluids?
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What is the continuity equation (differential and integral form) for incompressible fluids?
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How is the stress related to the stress tensor?
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What is Cauchy’s equation?
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What is the constitutive equation for a newtonian fluid?
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What is a newtonian fluid?
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How is the kinematic viscosity related to the dynamic viscosity?
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What are the units of the dynamic viscosity?
kg m^-1 s^-1
What are the Navier-Stokes equations?
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What are the kinematic and dynamic free surface boundary conditions?
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What is the reynolds number?
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What is the definition of the streamfunction?
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How can velocities be obtained from the streamfunction (cartesian)?
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How is the stream function related to the vorticity?
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What form is the CF of a constant coefficients ODE with real and equal roots?
(A+Bx)e^(lambda x)
What form is the CF of an Euler ODE with real and equal roots?
Aln(x) x^(lambda) + B x^(Lambda)
What is the form of the CF of an Euler ODE with complex roots?
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What is the form of the CF of a constant coefficients ODE with complex roots?
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How is the shear rate related to the rate of strain tensor?
What about the extensional rate of strain?
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In which direction is traction exerted?
exerted onto the fluid
What form of ansatz should we use for a periodically varying problem?
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What form of ansatz should we use for a similarity solution?
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When can a linearity and homogeneity argument be made?
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What are the parallel flow equations (cartesian)?
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What are the units of the streamfunction?
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What are the units of the vorticity?
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What are the units of force?
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What is the form of the non-dimensional N-S?
Everything dimensionless but the material derivative has the reynolds number as its coefficient.
In what case can we use the stokes equations?
What are they?
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How could we prove the relationship between the cartesian velocity components and the streamfunction?
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How is the vorticity related to the velocity?
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