Fluids- Fanno Flow Flashcards
When is wall friction significant?
For flows through long flow sections especially when the CSA is small
What are fanno flows?
Steady, one-dimensional, adiabatic flows of ideal gas with constant specific heats through a constant-area duct with significant frictional effects.
Formula for wall shear stress, τw
τw=(f/8)ρu^2
f is friction factor
How does stagnation pressure vary in fanno flow?
It decreases along the flow due to energy loss and entropy increase.
What does friction do to subsonic fanno flow?
Causes it to accelerate toward sonic velocity
What is maximum length for a duct?
Also called sonic length or critical length. Denoted by L*.
The length of the duct that causes the Ma to become exactly unity at the exit of the duct.
Where to find long formula for L*
Page 4 of notes or formula sheet.
f bar is friction factor maybe from moody diagram.
How to find duct length required to bring Ma from an initial value to another value not 1
Subtract the sonic lengths for the initial Ma and the Ma you want to get to.
Where to find Mach number relations for conditions along duct flow relative to its downstream sonic condition
Page 6 of notes or formula sheet
How to use relations of properties to sonic conditions formulae to determine the change in properties between any two states
Example is:
T2=T1(T2/T)/(T1/T)
What happens at the point of maximum entropy in fanno flow?
The Mach number Ma is 1
What happens to Ma, stagnation temperature, actual temperature, velocity, density in fanno flow?
Ma and velocity increase for subsonic but decrease for supersonic. Stagnation temperature remains constant but actual temperature decreases as velocity increases. Density also decreases as velocity increases.
What happens when length of duct is greater than L*?
Initial flow subsonic: inlet condition adjusts to give lower flow rate such that L=L*.
Initial flow supersonic: a shock wave forms such that the downstream subsonic flow returns to Ma=1 at the duct exit.
