GD Midterm 1 Review - Section 3 Flashcards
True or False:
The divergence theorem allows one to relate a volume integral into a surface integral.
True.
True or False
The stagnation enthalpy is constant for a moving fluid particle in steady adiabatic flow with no body forces.
True.
Section 3 PDF, page 12
Define Isoenergetic Flow.
In an isoenergetic flow, the stagnation enthalpy remains constant along any given streamline. This means that for a fluid particle traveling along a particular path, its total energy (stagnation enthalpy) does not change.
Define Homenergetic flow.
In a homenergetic flow, the stagnation enthalpy is uniform throughout the entire flow field. That is, every streamline in the flow has the same stagnation enthalpy, which implies that the entire flow originates from or is maintained by a region of constant stagnation enthalpy.
What is a barotropic fluid?
A fluid in which density is only a function of pressure.
Describe Kelvins circulation theorem.
Kelvin’s circulation theorem states that for a fluid moving under ideal conditions (i.e., inviscid flow with no viscosity, barotropic pressure-density relationship, and only conservative body forces such as gravity), the circulation around a closed material loop (a loop moving with the fluid) remains constant over time.
Kelvin’s circulation theorem is a cornerstone of classical fluid dynamics. It tells us that for an ideal, inviscid, barotropic fluid subjected only to conservative forces, the circulation around any material loop remains constant over time.
Describe Crocco’s theorem.
Crocco’s theory gives us a relation between kinematic properties of the flow (V and zeta) and thermodynamic properties (T, s, and h).
From Crocco’s theorem, fluid rotation can originate from what two sources:
- Gradients in stagnation enthalpy
- Gradients in entropy
True or False
From Crocco’s theorm, flow behind a shock must be rotational.
True.
Section 3 PDF, page 19
True or False
Steady inviscid flow with no body forces, the flow is irrotational if no gradients in stagnation enthalpy or entropy are present.
True
Section 3 PDF, page 19
True or False
A vector field with zero curl is called conservative.
True
True or False
The absence of vorticity (irrotationality) implies that the flow field is conservative, and in a simply connected region, any conservative field can be expressed as the gradient of a scalar potential function.
True
True or False
For an elliptic equation, the solution at any point on the interior of the domain of interest depends on the specified conditions on all boundaries.
True.
What type of flow phenomenon are parabolic equations often associated with?
Diffusion-type problems.
True or False:
For a hyperbolic equation, the solution at any point on the interior of the domain of interest depends on the specified conditions on all boundaries.
False.
The solution at any point depends only on a
limited region of the solution domain called the domain of dependence bounded by the upstream running characteristic curves.
Describe the eigenvalues of a system of first-order PDEs.
Hyperbolic: All eigenvalues are real and distinct.
Elliptic; Complex eigenvalues.
Parabolic: Repeated Eigenvalues
What does the gas dynamic equation describe?
The gas dynamic equation describes how energy changes due to flow acceleration are balanced by the compressibility of the fluid. It encapsulates the interplay between the convective transport of kinetic energy and the expansion or compression effects that arise in a compressible flow.
