400882 Introduction to Biomechanics - Fluid Mechanics

What is a Fluid?

Any substance that tends to flow or continuously deform when acted on by a shear force

• Liquids and gases

• Air and water

Explain what is meant by the term 'Relative Velocity'.

The velocity of a body in a fluid depends on the motion of the body and the fluid thus the term relative velocity is usually relative to the fluid but occasionally relative to another object.

Velocity relative to the fluid influences the forces acting on the object

Define Laminar Flow.

Smooth parallel layers of fluid

The pathways of the fluid particles don't cross

Explain what Turbulence is and how it is created.

As velocity relative to the fluid increases, flow of the fluid becomes turbulaent (random/swirling)

Turbulent flow under hand / drag over hand

Define Density; provide its symbol/s and unit of measurement.

• Density = mass per unit of volume

• Density ρ (rho) = m / v

• Units = kgm³

List in order of most dense to least dense the following substances: Muscle, Water, Fat, Air and Bone.

1. Bone 1100 - 1800 kgm³

2. Muscle 1030 - 1090

3. Water 1000

4. Fat 950 - 990

5. Air 1.21

Define Specific Weight; provide its symbol/s and unit of measurement.

Weight per unit of volume

γ = weight/vol [Specific wt γ (gamma) = weight / volume]

What affect would increasing the density and specific weight of a fluid have on the force exerted by that fluid on another body?

↑ density & specific weight of the fluid → ↑ magnitude of forces exerted by the fluid on the object

Viscosity refers to what?

Measure of a fluids internal resistance to flow

Increasing the viscosity of a fluid would result in what occurring?

↑ viscosity → ↑ forces by fluid on object

This is not related to density

In what ways do temperature and pressure influence the density and viscosity of fluids?

• ↑ T → ↓ density & ↓ viscosity

• ↑ P → ↑ density & ↑ viscosity

Define Buoyancy.

Fluid force that acts vertically upward

Archimedes' Principle states that...

The buoyant force acting on an object in a fluid is equal to the weight of the fluid displaced by the body

Fb = Vdγ

• Fb = buoyant force

• Vd = Volume displaced

• γ = specific weight of fluid

In which direction do buoyant forces always act?

Buoyant forces always act vertically upward

What affect does increasing the density of a fluid have on the buoyant force that fluid is capable of exerting?

↑ density of fluid → ↑ Fb (the sea vs fresh water)

The Centre of Volume refers to what?

Pt about which a body's volume is equally balanced, through which the buoyancy force acts

Different to COM or CG

What determines whether a body will float or not?

Flotation depends on relationship between buoyancy and weight

When Fb & W are the only two forces

• Fb = W will have equilibrium (static) → Float

• W > Fb → Sink

For most swimmers, floating occurs when?

...

Why don't most people float level with their body parallel to the surface of the water?

...

What is Drag and in which direction does it usually act?

Drag is force caused by dynamic action of a fluid

Usually resists movement of an object through fluid

From the formula for drag, list and explain the affect these four factors have on the magnitude of drag force.

FD = ½ CDApv2

• FD = drag force

• CD = coefficient of drag (an index of a body's ability to generate fluid resistance)

• ρ = fluid density

• Ap = projected area of the body or surface area of body ⊥ to fluid flow

• v = velocity relative to fluid

What affect would high altitude have on total drag?

Air density ↓ with altitude thus ↓ FD

Name the THREE components of drag.

• Surface drag

• Form drag

• Wave drag

What two other names are often given to Surface Drag?

Surface friction or Viscous drag

Define and explain Surface Drag.

...

Explain how surface drag is minimised in some sports.

...

What two other names are often given to Form Drag?

Profile or pressure drag

Define and explain Form Drag.

When boundary layer is primarily turbulent - form drag predominates

When a body moves fast enough to cause a pocket of turbulence there is an imbalance in pressure surrounding the body

• Upstream → high pressure

• Downstream → low pressure

The magnitude of form drag is dependent on what 3 things?

• Relative velocity

• Magnitude of pressure gradient

• Surface area ⊥ to flow (cross-sectional area)

Explain how Streamlining can minimise form drag and provide 2 examples.

• ↓ cross-sectional area which minimises turbulence & hence ↓ form drag

• Competitive cyclists, skaters & skiers will assume a streamlined body position

• Wet suit - buoyancy to ↑ form drag

• Slightly rough surface ↓ form drag (golf ball dimples)

• Race cars, yacht hulls, cycling helmets = streamlining

How does the tear drop shape of a track cycling helmet decrease from drag?

...

How do the dimples on a golf ball decrease from drag?

...

Explain how Wave Drag is generated.

• Acts at the interface between 2 different fluids e.g. air and water

• As a body segment is moved along, near or across the air water interface a wave is created in the more dense fluid.

• The reaction force of the water on the body constitutes wave drag

Explain how wave drag can be minimised.

• Wave drag ↑ with greater up and down motion of the body & with ↑ swimming speed

• Skilled swimmers produce a smaller bow wave than unskilled swimmers at the same speed presumably due to less up & down motion and better technique

• Swimming pool lane ropes are designed to minimise waves by dissipating moving surface water.

What are Lift Forces and in which direction do they act?

Lift force = a force acting on a body in a fluid that acts in a direction ⊥ to the fluid flow

Bernoulli's Principle states that ...

• LP = HV (low pressure = high velocity)

• HP = LV (high pressure = low velocity)

How do foil shapes provide lift forces?

Fluid flowing over curved surfaces accelerates → increased velocity flow and result in lift force

Difference in velocity → a pressure difference Low pressure on top and higher pressure underneath causes lift force ⊥ to the foil to be directed towards the region of low pressure

How can lift force be increased?

• CL is based on shape

• Greater velocity of foil relative to fluid → ↑ lift

• ↑ surface area of flat side of foil → ↑ lift

• ↑ density → ↑ lift

Define Angle of Attack.

Is the angle between the longitudinal axis of a body & the direction of fluid flow

• Important in launching a lift producing projectile for max range

• Balance of lift and drag depends on size, shape and material of object

A +ve angle of attack is necessary to generate a lift force

Explain the Lift / Drag Ratio.

As angle of attack ↑ then surface area to fluid flow ↑ ↑ drag

Angle too steep - fluid cant flow along curved surface and lift not created

What is a Magnus Force and under what conditions can it be observed?

• Magnus force is a lift force directed from the high pressure region to the low pressure region.

• When object spins in a fluid, molecules of fluid on one side collide with molecules in fluid free stream → causing a region of relatively low velocity and high pressure

• On the opposite side boundary layer moves in same direction as fluid flow → region of high velocity and low pressure

• ∴ spin and its effect on pressure zones are

HV = LP

LV == HP

Which motion results from a Magnus force being applied to a ball?

Progressive deviation in the direction of spin

List TWO ways that the Magnus force experienced by an object can be increased.

...

Name and explain two theories on how swimmers propel themselves through water.

• Propulsive drag theory:

Based on Newton's 3rd law of motion

As swimmers hands and arms move backwards through water the forward directed reaction force produces propulsion

• Propulsive lift theory:

Swimmers use a foil like shape of hand

Rapid lateral movements through water generates lift.