# Materials

Fluid Flow and Strength of Materials

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## Fluids

Fluids

A fluid is defined as any substance that can flow

Density (kgm-3) = mass (kg) / volume (m^3)

Upthrust = density fluid x volume x gravity

Laminar flow - happens at a slow speed

- flow in layers with no mixing

- velocity at any point is constant

Turbulent flow - happens at a high speed

- mixing of layers

- forms eddies

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## Viscious Drag

Viscous Drag

When in liquid, and you increase the temperature, viscosity decreases

When in gas, and you increase the temperature, viscosity increases

A way of measuring viscosity is by rolling a tin down a ramp

Stokes law can only be applied if object is a small sphere and moving at a slow speed

v term = 2r^2g(ps - pr) / 9 x viscosity

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## Hookes Law

Hookes Law

F = kx

F = force (N)

K = spring constant (Nm-1)

x = extension (m)

The graph must be a straight line or there must be no y intercept, so the line goes through 0, if one of these are achieved then the graph obeys hookes law

Elastic Strain Energy

Eel = 1/2Fx = 1/2kx^2

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## Young Modulus

Young Modulus

Stiffness depends on:

• cross sectional area and length
• artefact (varies with dimension) property - changes accordingly to how much material there is

Stress (Nm-2) = F / A

Tensile strength - greatest stress before facturing

Strain = x / L

Tensile strain - increase in extension

Compressive strain - decrease in extension

Young modulus  = tensile stress / tensil strain  = tensile force / area . / extension / original length

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## Young Modulus

Young Modulus Graph

Linear region - extension inversely proportional to force (stress), point at which this behaviour stops is called proportionality limit

Proportionality limit - stress is no longer proportional to strain after this point

Elastic limit - at this point, material stops behaving elastically and begins to behave plastically, stress is removed and material does not return to original length

Yield point - point the material shows large increase in strain for a small increase in stress - plastic deformation begins

Plastic region - extension increases rapidly for small increase on force in this region

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## Properties of Materials

Brittle - undergoes no or little plastic deformation before breaking or tends to break when subject to large impact forces

Hard - difficult to scratch or indent

Tough - undergoes a large plastic deformation before breaking or withstands large impacting forces / shocks

Ductile - undergoes large plastic deformation before breaking

Malleable - undergoes large plastic deformation before cracking

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