Lecture 4 Flashcards

(20 cards)

1
Q

What law does the momentum equation take into account?

A

Newton’s 2nd Law; F=ma.

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2
Q

What 2 types of forces is the “force” in “F=ma” made up of? What are the definitions of these and give 3 examples of one of them, and 2 types of another.

A

Body / Volume forces: acting on volumetric mass of fluid element, “at a distance”. Eg. Gravitational; Electric; Magnetic.

Surface forces: act on surface of fluid element. Two types: pressure and viscous (shear/normal) stress.

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3
Q

What are the pressure forces within the surface forces imposed by?

A

By the outside fluid surrounding the fluid element (“thermodynamic pressure” associated with particle collision at microscopic level).

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4
Q

What are the viscous (shear/normal) stresses associated with the surface forces imposed by? How do these vary from the pressure forces.

A

Also by outside fluid, where it “tugs” or “pushes” on the surface by means of friction.

Pressure forces are of a thermodynamic nature; viscous stresses are due to viscosity.

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5
Q

How does the shear stress arise in a flow?

A

Different flows moving at different velocities exert shear stresses on each other.

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6
Q

What are viscous shear and normal stresses related to? What do they depend on?

A

The time rate of change of the deformation of the fluid element.

Depend on velocity gradients.

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7
Q

Normal vs Shear Stress: what different things are they related to?

A

Shear: time rate of change of shearing deformation of fluid element.

Normal: time rate of change of volume of fluid element.

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8
Q

Which direction does each stress (normal and shear) deform the fluid element?

A
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9
Q

How do the magnitudes of normal stresses and shear stresses compare?

A

Normal stresses are typically smaller

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10
Q

Explain the flow chart that summarises all forces acting on a body for the momentum equation.

A
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11
Q

What is the notation for the body force acting in the x-direction for the momentum equation?

A
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12
Q

Roughly outline the surface force diagram for momentum equation in x-direction. IMPORTANT: what’s the convention for labelling directions?

A
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13
Q

How can you tell whether a stress is normal or shear from the sign convention?

A

If subscript is the same; normal.

If different; shear.

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14
Q

What is the total LHS (forces) of the equation for momentum equation? What two things is the total force broken down into?

A
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15
Q

What is on the RHS (ma) of the momentum equation in the x-direction, for the Lagrangian model, and why?

A

Mass = density * volume

Accel. = Du/Dt because it’s the Lagrangian model, so substantial derivative used due to the moving fluid.

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16
Q

Final form of x-component of momentum equation, before tau simplification.

17
Q

With the x-direction derived, how would the y and z-directions look? What are these called? What is the next step in the derivation?

A

Navier-Stokes equation

Still have to substitute to replace the tau (stresses)

18
Q

What does this equal for incompressible flow and why?

A

0, because continuity

19
Q

Final form of momentum equation with accel., force, mass labelled.

20
Q

Final form of momentum equation with terms labelled.