fluid flow motion of objects in fluids how can a plane fly? why does a cricket ball swing or a...
TRANSCRIPT
FLUID FLOW MOTION OF OBJECTS IN FLUIDS
How can a plane fly?
Why does a cricket ball swing or a baseball curve?
Why does a golf ball have dimples?
web notes: lect6a.ppt flow4.pdf flight.pdf
Lift FL
drag FD
Resultant FR
Motion of object through fluid
Fluid moving around stationary object
FORCES ACTING ON OBJECT MOVING THROUGH FLUID
C
D
BA
Uniform motion of an object through an ideal fluid ( = 0)
The pattern is symmetrical
FR = 0
Drag force
frictional drag (viscosity)
pressure drag (eddies – lower pressure)
low pressure region
high pressure region
rotational KE of eddies heating effect increase in internal energy temperature increases
Drag force dueto pressure difference
NO CURVEDrag force is opposite to the direction of motion
motion of air
motion of object
low pressure region
high pressure region
Drag force dueto pressure difference
v
v
flow speed (high) vair + v reduced pressure
flow speed (low) vair - v increased pressure
vair (vball)
Boundary layer – air sticks to ball (viscosity) – air dragged around with ball
MAGNUS EFFECT
motion of air
motion of object
Velocity profile around ball
Ball moving to left and rotating clockwise Ball moving to left and rotating clockwise
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Professional golf drive
Initial speed v0 ~ 70 m.s-1
Angle ~ 6°
Spin ~ 3500 rpm
Range ~ 100 m (no Magnus effect)
Range ~ 300 m (Magnus effect)
Golf ball with backspin (rotating CW) with air stream going fromleft to right. Note that the air stream is deflected downward with a downward force. The reaction force on the ball is upward. This gives the longer hang time and hence distance carried.
The trajectory of a golf ball is not parabolic
How can a plane fly?
lift
Direction plane is moving w.r.t. the air
Direction air is moving w.r.t. plane
low pressure drag
attack angle
lift
downwashhuge vortices
momentum transfer
low pressure
high pressure
(a)
vSvS
(b)counter circulation
Startingvortex
Trailing tip vortices
Starting vortices
Circulation aroundan airfoil
Trailing tip vortices
FLift = CL ½ vs2 A
