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**Materials Fluids and Fluid Flow 1 Fluids and Fluid Flow 2**

Force and Extension Stress, Strain, and the Young Modulus

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**Turbulent + Laminar Flow**

Laminar /Streamline Flow– layers do not cross each others paths. Occurs at lower speeds. Turbulent Flow – layers cross and mix. Occurs at higher speeds.

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**Viscous Drag Force The force of friction caused by a flowing fluid**

Is in the opposite direction to movement

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Upthrust Force Upthrust is a force that acts vertically upwards on an object in a fluid Upthrust = weight of fluid displaced

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Density A measure of how close-packed the particles are in a substance. EG: gases are much less dense than solids and liquids because their particles are more widespread.

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Terminal Velocity As an object falls it’s speed increases. The drag on it will also increase. Eventually a speed is reached where the drag force = the weight. As there is no net force on the object, the acceleration will be zero.

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**Viscosity The higher the viscosity of a fluid, the slower it flows.**

Viscosities of most fluids decrease as the temperature increases. Fluids generally flow faster if they are hotter.

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Stokes’ Law Calculates the drag force on a sphere as it travels through a fluid. F = viscous drag force acting on the sphere r = radius of the sphere n = viscosity of the fluid v = velocity of sphere

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**ALL Forces on a Falling Sphere**

Stokes’ Law + Upthrust = Weight

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Hooke’s Law The extension of a sample of material is directly proportional to the force applied. Hooke’s Law does not apply to all materials k = stiffness = the gradient = F/x

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**Force v Extension/Compression Graphs**

Limit of Proportionality – The point beyond which force is no longer directly proportional to extension (line is no longer straight) Elastic Limit – This is when the force is taken away, the material no longer goes back to its original length Yield Point – Material shows a greater increase in extension for a given increase in force Ultimate Tensile Stress – The maximum stress that the material can withstand Breaking Stress – the point at which the material breaks

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**Ultimate Tensile Strength: the maximum stress (force) a material can withstand.**

Breaking Stress: the stress at which the material breaks. Can be the same as UTS.

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**Stress and Strain Stress (N/m2) Strain (no units)**

= Force (N) / Area (m2) Strain (no units) = Extension (m) / Original Length (m)

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**Young Modulus YM = FL/EA**

YM = Stress/Strain YM = (F/A)/(E/L) YM = FL/EA YM = the gradient of a stress/strain graph The greater the YM (the steeper the gradient) the stiffer the material. Ie: the less it stretches for a given force.

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**Elastic and Plastic Deformation**

At point A, Masses (Force) are unloaded from the material. Plastic deformation has occurred as the material has not gone back to it’s original length.

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**Material Characteristics**

Brittle: Breaks suddenly without deforming plastically. Follows Hooke’s Law until it snaps. Glass. Ductile: Undergos plastic deformation by being pulled into wire. Retains strength. Copper. Malleable: Undergos plastic deformation by being hammered or rolled into shape. Loses strength. Gold. Hard: Resist plastic deformation by compression or scratching rather than stretching. Diamond. Stiff: Measure of how much a material stretches for a given force. Bamboo. Tough: Measure of the amount of energy a material can absorb before it breaks. Toffee.

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**Elastic Strain Energy Plastically deformed material:**

E = ½ x Force x Extension (Similar to W=Fs) Elastically deformed material: E = area under force/extension graph

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