Dynamic Fluid Forces

Forces that result when an object moves through a fluid, or when a fluid moves past an object.

Pages 197-210 in book

Dynamic Fluid Force

• Arises due to the relative motion of an object in a fluid. There must be motion!!

• F ½CDAv2

• CD = Drag coefficient

= Fluid density

• A = Surface area perpendicular to flow

• v = Relative velocity of object and fluid

Water Skiing

Vi

Water Particle

Vf

Two things happen to the particle of water when it comes in contact with the ski.1. It’s direction will change2. It’s speed will be reduced

This means the particle underwent acceleration, which means forces must have been acting on the particle.

The Force on the Water Particle

Vi

VfV

V = Vf - Vi

F = maAcceleration is change in velocity over time

F = m (V/t)

The force must act in the same direction as the acceleration vector, and the acceleration vector must act in the same direction as the change in velocity vector determined above.

F

The Force on the Ski (Dynamic Fluid Force)

Newton’s 3rd Law: for every force there is an equal and opposite force

We’ve determined the force of the ski on the water, therefore we now know the force of the water on the ski.

F

This force can be broken down into components that act perpendicular and parallel to the direction of motion.

Lift: Always perpendicular to motion. Not necessarily in the up direction.

Drag : Always parallel to motion.

Drag Force

• Surface Drag: Viscous drag, or skin friction

• Form Drag: Shape, profile, or pressure drag

Surface Drag

Boundary Layer: Layer of fluid that clings to and moves with the object. This layer produces an external force on the object.

The boundary layer has an external force acting on it from the adjacent layer of fluid. This process eventually dissipates.

The roughness of the surface and how long the air molecules are in contact are large influences on surface drag.

Form DragForm drag is influenced by the shape and the size of the object. In particularly, it is influenced by the cross-sectional area of the object that is perpendicular to the relative motion.

AirMolecules

Big deflection means a big force must have caused the change in direction.

Form Drag

The relative shape of the object to the direction of motion affects the movement of the air molecules.

A large blocking shape results in large changes to the direction of the air molecules. The larger the change in direction, the larger the force required. This means large reaction force back on the object.

Form Drag and Fluid FlowAir molecules hitting the leading surface increase form drag

Air molecules hitting the trailing surface reduce from drag, because they have components directed towards the front of the object.

The type of fluid flow determines whether air molecules hit the trailing surface.

Laminar: Molecules remain close to surface of object

Turbulent: Molecules deflected away from object and therefore do not hit the trailing end of the object.

TURBULENT FLOW

LAMINAR FLOW

BASEBALL LAMINAR FLOW

GOLF BALL LAMINAR FLOW

Better than baseball

TENNIS BALL : MORE TURBULENT

No Spin:New Fuzzy Ball

No Spin:Old Smoother Ball

Tennis Ball Hit with Top Spin

Direction of Flight

Final path of air

Tennis Ball Hit with Back Spin

Direction of Flight

Final path of air

Trade Off Between Surface Drag and Form Drag?

• Check out Spoiler aerodynamics webpage in Favorites

Flow Visualization Of Wake Asymmetry on Spinning Golf Ball