Fluids and Aerodynamics

F1– Buoyant Forces

F2– Non-Viscous Fluid Flow

F3 – Viscous Fluids

F4– Explaining Lift using

Newton and Bernoulli

Flying

F1 Buoyant Forces

An upthrust is provided by the fluid displaced by a submerged or floating object.

Archimedes’ Principle– The upthrust on a body partially or fully submerged in a fluid is

equal to the weight of the fluid displaced by the body. The Principle of Flotation

– A body floating in a liquid always displaces its own weight of the liquid.

The upthrust on a floating object acts at the centre of mass of the displaced fluid ( centre of buoyancy )

The stability of a floating object is determined by the relative positions of metacentre and the centre of mass of the floating object.

F2 Non-Viscous Fluid Flow

Motion Of An Ideal Fluid– Steady ( laminar , streamline ) flow

Streamlines can be used to define a tube of flow. The equation of continuity is Av = constant for the

flow of an ideal, incompressible fluid. Appreciate that the equation of continuity is a form of

the principle of conservation of mass. The Bernoulli Effect

– Pressure differences can arise from different rates of flow in a fluid.

F2 Non-Viscous Fluid Flow

Derive and use Bernoulli equation– p1 + 1/2( v1

2 ) = p2 + 1/2 ( v2 2 ) = constantwhere p is the pressure is the fluid density and v is the velocity of the fluid

Appreciate that Bernoulli Equation is a form of conservation of energy

Apply Bernoulli effect in– Spinning balls in sport– atomisers– flow of air over an aerofoil

F3 Viscous Fluids

Viscous forces in a fluid cause retarding force to be exerted on an object moving through a fluid.

In viscous flow, different layers of the liquid move with different velocities.

Stokes’ Law states that F = Arv where A is a dimensionless constant, for the drag force under laminar conditions in a viscous fluid.

Use Stokes’ law to explain quantitatively how a body falling through a viscous fluid under laminar conditions attains a terminal velocity.

F3 Viscous Fluids

At sufficiently high velocity, the flow of viscous fluid undergoes a transition from laminar to turbulent conditions.Under normal conditions, the drag force resisting motion is proportional to the velocity but under turbulent conditions, the drag force resisting motion is proportional to the square of the velocity.

The onset of turbulence is determined by the Reynolds’ number Re = vr / – For fluid flow in a tube or channel– For the motion of an object relative to a fluid. Note :

if Re < 2000 , the fluid flowing in the tube or channel is steady. If Re > 2000 , the fluid flow in the tube or channel is turbulent

F4: The lift on an aerofoil

There are two ways to think about the lift on an aerofoil:

1. Using Newton’s Laws

2. Using Bernoulli’s Equation

F4: Explaining lift using Newton

F4: Explaining lift using Newton

The aerofoil acts to redirect the direction of air passing over it.

F4: Explaining lift using Newton

This results in a net force upwards (of the aerofoil on the air above) which is called lift

F4: Explaining lift using Bernoulli

The explanation using Bernoulli’s principal involves the fact that the air moves faster over the top of the aerofoil compared to air moving underneath it.

This is based on the equal transit time assumption

F4: Explaining lift using Bernoulli

This difference in velocity means that there is a difference in pressure above and beneath the wing.

This results in Lift.

End Note

The belief that rear spoilers significantly increase car performance by aiding it’s aerodynamicy is dubious at best