# SOLIDS: Strain is related to stress. For Hookean or linear elastic solids σ =E ε , where

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500.101500.101

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500.101500.101SOLIDS: Strain is related to stress. For Hookean or linearelastic solids

σ=Eε, where

ε is strainE is Young’s modulus σ is stress (force/area)

FLUIDS: Strain rate is related to shear stress. For Newtonian fluids

τ = μ du/dy, where

τ is shear stress,μ is viscositydu/dy is velocity gradient

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500.101500.101

Viscosity behaviorof fluids

Newtonian. Shear thickening. Shear thinning.

Thixotropic.Bingham plastic

Magnetorheological fluid

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EQUATIONS

i

j

j

i

xu

xup

DtVD

Re1

0 V

t

Momentum

Continuity

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BERNOULLI EQUATION

constgzvpt

2

21

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500.101500.101Dimensionless quantities

Reynolds Re LV/ν Inertial force/viscous force

Rossby Ro V/(2LΩ sin θ) Inertial force/Coriolis force

[Drag coefficient] Cd (ρ’-ρ)Lg/(ρ’V2) Drag force/inertial force

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500.101500.101 Oceanography

Meteorology

Aeronautics

Biomedical fluid mechanics

Convective heat transfer

Turbulence

Acoustics

Powerless pump

Other. . .

Fluid Fluid mechanicsmechanics

500.101500.101Oceanography

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500.101500.101Meteorology

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500.101500.101Biomedical fluids

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500.101500.101

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500.101500.101Aeronautics

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500.101500.101Turbulence

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500.101500.101Water delivery

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500.101500.101Acoustics

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RECORD FUEL PRICES PLACE STRESS ON OCEAN SHIPPING May 2, 2008 Shipping lines worldwide are struggling as crude oil prices topped an unprecedented US$119 per barrel this week, in turn pushing marine bunker fuel prices up past $552 per ton – a $26 per ton increase since the end of March alone. Bunker prices have risen 87% since the beginning of 2007. Fuel costs represent as much as 50-60% of total ship operating costs, depending on the type of ship and service.

.

.

. With the cost of bunker fuel at $552 per ton, with fuel consumption at 217 tons per day, and a 14 day voyage, a single round trip voyage for this one vessel would produce a fuel bill of $3,353,952.

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500.101500.101SkySails flies 100-500m abovesea surface

Generates about 1.5 hp/m2

Largest offering 5000 m2

Estimated fuel saving Rotterdam/NY 27%

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500.101500.101

Convective cooling

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500.101500.101Engines

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500.101500.101Water jet cutter withinjected abrasive(40K psi)

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500.101500.101Power generation fromocean waves