Fluids- External Flow and Drag Flashcards
What is drag?
The force a flowing fluid exerts on a body in the flow direction
What is friction drag?
Drag force depending on wall shear. Depends on surface area parallel to flow.
What is pressure drag?
Drag force acting that depends on the pressure difference between the front and back faces of an object. The area of low pressure sucks the object back into it. Depends on projected frontal area.
What is velocity boundary layer?
The region of flow above the plate bounded by δ in which the effects of the viscous shearing forces caused by fluid viscosity are felt
How is δ defined?
The distance at the surface at which u=0.99V
Difference between boundary layer region and irrotational flow region
In boundary, viscous effects and velocity changes significant. In irrotational, frictional effects negligible and velocity essentially constant.
Formula for displacement thickness
δ*=S(1-u/U)dy
From 0 to δ
Formula for momentum thickness
Θ=S(u/U)(1-u/U)dy
From 0 to δ
Boundary layer equation
τw/ρU^2=dΘ/dx
Formula for wall shear stress for laminar flow over plate
τw=2μU/δ
Formula for δ over x (laminar)
δ/x=5.5/Re^1/2
Formula for skin friction coefficient Cf
Cf=0.73/Re^1/2
How is total drag force defined for laminar flow over flat plate?
D is integral of wall shear stress with respect to x times width of plate
Formula for friction coefficient for laminar flow over plate
CD=1.328/Re^1/2
=D/(0.5ρU^2bL)
Formulae for δ Cf and CD for turbulent flow over smooth plate
See page 10
How to use analog of Moody chart for pipe flows for external flow
Find L/ε (length of plate over roughness) to know which line to use. Go up from Reynolds number to that line and find Cf. Or use formula if fully rough on page 10.
Formula for CD for friction and pressure drag
CD=FD/(0.5ρV^2A)
A is parallel area for friction
A is frontal area for pressure
How do different types of drag forces and coefficients combine
Added linearly
When does a body in free fall reach terminal velocity?
When drag force equals weight minus buoyant force.
Describe flow separation
At sufficiently high velocities, the fluid stream detached itself from the surface of the body when the surface changes level. Location of separation point depends on Re, ε and level of fluctuations in the free stream.
Separated region
Region between body and fluid stream when the fluid separates. It is low pressure region behind the body where recirculation and backflows occur
How does size of separated region relate to pressure drag?
Larger separated region means larger pressure drag
Wake
The region of flow trailing the body where the effects of the body on velocity are felt
How does streamlining work?
Decreases pressure drag by delaying boundary layer separation and reducing pressure difference between front and back of the body. Height of body is D, length is L.
How do friction and pressure drag vary with D/L?
Pressure drag increases with increasing D/L
Friction drag decreases with increasing D/L
There is value of D/L where total drag is at minimum
Stokes law
FD=3πμVD
Applicable to dust particles in air and suspended solid particles in water
How does superposition work?
Consider a complex body as a combination of simple bodies and add the individual drag coefficients to get approximate value.
Why is there a dip in CD for flow over a smooth cylinder or sphere at high Re?
Due to flow separation point. The laminar boundary layer becomes turbulent so clings on to body longer before detaching so there is less pressure drag.
What happens to CD for smooth sphere and cylinder as Re increases?
See top of page 19 for details.
How does roughness impact CD for spheres and cylinders?
See bottom of page 19 for graph. Depends on Re
