fluid flow motion of objects in fluids

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 airmotion 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 airmotion 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)vS

vS

(b)counter circulation

Startingvortex

Trailing tip vortices

Starting vortices

Circulation aroundan airfoil

Trailing tip vortices

FLift = CL ½ vs2 A