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Geodynamics www.helsinki.fi/yliopisto
Geodynamics
Basics of fluid mechanics Lecture 9.1 - Introduction to fluid mechanics
Lecturer: David Whipp [email protected]
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Goal of this lecture
• Introduce the basic concepts of fluid mechanics and where it can be applied
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Fluids and the Earth
• Fluid: Any material that flows in response to an applied stress
• Differences between solids and fluids
• Rheological (or constitutive) law: An equation relating stress to strain rates in a fluid
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Solids Fluids
Strain from being stressed Continuous deformation under applied forces
Stresses related to strains Stresses related to rates of strain
Strain result of displacement gradients Strain result of velocity gradients
Newtonian (or linear) fluid
• A Newtonian fluid is a fluid in which there is a linear relationship between the rate of strain and the applied stress
• What would this relationship look like as an equation?
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Material Approximate Viscosity [Pa s]
Air 1x10-5
Water 1x10-3
Ice 1x1016
Rock Salt 1x1017
Granite 1x1020
Newtonian (or linear) fluid
• A Newtonian fluid is a fluid in which there is a linear relationship between the rate of strain and the applied stress
• What would this relationship look like as an equation?
• The proportionality constant 𝜂 is known as the dynamic (or shear) viscosity
• Dynamic viscosity has units of [Pa s]
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� / "̇ � = ⌘"̇or
• The concepts of fluid mechanics are based on conservation of
• mass
• momentum, and
• energy
• Conservation of mass, momentum and energy are combined with rheological laws to describe fluid movement under an applied force
Fluid mechanics
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Magma migration and flow
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Folding of rock
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Mantle convection
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Fig. 1.61, Turcotte and Schubert, 2014
Let’s see what you’ve learned…
• If you’re watching this lecture in Moodle, you will now be automatically directed to the quiz!
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