Incompressible Flow Flashcards
(25 cards)
What two principles are the basis of incompressible fluid flow
Mass in conserved - continuity
Newton’s 2nd law - Navier-Stokes equations
What does continuity mean in incompressible flow
Density is constant so equation simplifies to sum of velocity derivatives in each coordinate direction
What is convection
Mass/energy process due to bulk motion of a fluid
What is diffusion
Spreading of concentration until gradient is 0
What does Fick’s law of diffusion mean qualitatively
Mass flux of ink across a unit area by diffusion is proportional to the concentration gradient and diffusivity of the ink
Diffusion always opposes direction of gradient
What does the pollutant transport equation mean
For steady incompressible flow the total net mass flux into a control volume should be 0 to conserve mass
Why are boundary conditions needed everywhere in a pollutant transport problem
Diffusivity means a disturbance can be felt everywhere
When can a streamline be expressed as a function of x and y
As long as the flow field it describes satisfies the continuity equation and the definition of a streamline
What is a stream tube
The area bounded by two streamlines
What is the change in value of the stream function between two streamlines equal to
Numerically, the volume flow rate between the two streamlines
What is Stokes flow
Steady incompressible flow of very low speed around a sphere
Reynolds number «_space;1
What does a low Reynolds number mean qualitatively
The inertial force of the flow is small compared to the viscous force
Convection term (inertial) can be ignored
What is the pressure force balanced by in the Stokes equation
Shear stress only
Where does the pressure peak in Stokes flow
At the stagnation points
Where does the shear stress (friction force) peak in Stokes flow
On the top and bottom where the velocity gradient is the highest
Why are streamlines symmetric fore and aft in Stokes flow
Weak convective acceleration
What is the pressure distribution on the surface in Stokes flow
Linear
What happens to flow speed in Stokes flow
Slowed all the way to far region
Where is the acceleration zero in Stokes flow
Near the top of the sphere
What is ideal flow on a sphere
Steady incompressible and inviscid flow
No surface friction
What approach is taken to solve ideal flow
Find a stream function that satisfies the flow conditions first
Use stream function to work out velocity and pressure distributions
NS equation reduces to Bernoulli’s equation for inviscid flow
What is superposition
If two sets of solutions to a linear equation are known, the solutions can be summed to find a new solution to the equation
Where is the maximum speed in ideal flow on a sphere
Top of surface
What is the pressure distribution fore and aft of a sphere in ideal flow
Symmetric as there is no drag force
