When is a flow physically possible?
When $ \nabla • \vec{v} = 0 $
What is the formula for Reynold's number?
$ R_e = \frac{\rho_\infty v_\infty c}{\mu_\infty} $
What are the SI units of viscosity?
$ \frac{kg}{m•s} $
How can we calculate viscosity given a temperature?
Sutherland's Law$$ \mu (K) = 1.458 [\frac{T^{1.5}}{T+110.4}]E-6 \frac{kg}{m•s} $$$$ \mu (°R) =2.27 [\frac{T^{1.5}}{T+199}]E-8 \frac{slug}{ft•s} $$
When is a flow irrotational?
When the vorticity, $ \vec{\zeta} = \nabla \times \vec{v} = 0 $
What is the formula for divergence?
$$ \nabla • \vec{v} = \frac{\partial v_x}{\partial x} + \frac{\partial v_y}{\partial y} + \frac{\partial v_z}{\partial z} $$
What is the gradient of $ \nabla \rho $?
$$ \nabla \rho = \frac{\partial \rho}{\partial x} \hat{i} + \frac{\partial \rho}{\partial y} \hat{j} + \frac{\partial \rho}{\partial z} \hat{k} $$
How is curl mathematically depicted?
$$ \nabla \times \vec{v} $$
How do we write the substantial derivative for density?
$$ \frac{D \rho}{Dt} = \frac{d \rho}{dt} + (\vec{v} • \nabla) $$
How can we start out calculating the equation for streamlines?
$$ \frac{dy}{dx} = \frac{v}{u} $$
For a constant $ \psi $, what is the slope of the streamline?
$$ (\frac{dy}{dx})_{\psi = const} = \frac{v}{u} $$
For a constant $ \phi $, what is the slope of the streamline?
$$ (\frac{dy}{dx})_{\phi = const} = -\frac{u}{v} $$
How does angular velocity ($ \omega $) relate to vorticity ($ \zeta $)?
$$ \zeta = 2 \omega $$
What are the primary dependent variables for compressible flow?
$$ P, \vec{v}, \rho, e, T $$
How is density different in compressible flow than in incompressible flow?
$$ \rho \neq constant $$
What does isentropic mean?
It means a process is adiabatic (no heat transfer) and reversible (change in entropy is zero).
When can the velocity potential equations for perturbations be used?
When (1) small perturbations, small AoA, and thin airfoil, and (2) when in subsonic and supersonic flow (not valid for transonic or hypersonic).
What is the most accurate correction equation between Prandtl-Glauert, Karmen-Tsien, and Laitone's?
Karmen-Tsien
For subsonic flow, what is the Prandtl-Glauert correction factor?
$$ \frac{1}{\sqrt{1 - M^2_{\infty}}} $$
For supersonic flow, what is the Prandtl-Glauert correction factor?
$$ \frac{1}{\sqrt{M^2_{\infty} - 1}} $$
What is the critical Mach number?
As the Mach number is increased for an aircraft, when there is a minimum pressure on the wing with a local Mach number equal to 1, the aircraft's current Mach number will be the critical Mach number, $ M_{cr} $.
What is a Sears-Haack body?
An ideal volume distribution for limiting $ C_{D_o} $.
When adding a wing to a fuselage modeled as a S-H body, what method can be used to maintain an ideal shape?
The area rule.
How is Mach angle $ \mu $ calculated?
$$ \mu = \sin^{-1}(\frac{1}{M_{\infty}}) $$
What do supercritical airfoils work to do?
Increase the distance (in terms of Mach number) between critical Mach number and drag-divergence Mach number.