ERTH 430: Fluid Dynamics in Earth Systems Pre-class Quiz #1: Continuum Hypothesis, Flow Distortion, and Solving the Governing Equations

This is a "preview" version of Pre-class Quiz #1. The preview version is suitable for printing and leisurely inspection before you submit your answers to the interactive or "live" version—that is, the real thing. When you feel ready to submit your answers, go to iLearn's ERTH 430 "Pre-class Quizzes" section, select the interactive version, and follow its instructions.

(Responses must be submitted via iLearn by 9 a.m. on Wednesday, Aug. 30.

Description: The questions below are based on Reading Assignment #1.

Questions:

(1) Multiple Choice. What is the continuum hypothesis, on which the governing equations for fluid dynamics are based? (Pick the one best answer.)

1. The assumption that fluids consist of discrete (separate) bits of matter (such as molecules), idealized as infinitesimal points of mass.
2. The assumption that the properties of a fluid (such as its temperature, density, and velocity) are spatially continuous (not discrete) within the fluid.
3. Mass (matter) can be neither created nor destroyed, but instead is "conserved".
4. At any particular point within a fluid, the fluid for all practical purposes can be treated as if it extends indefinitely, without bounds.

(2) Multiple Choice. When forces associated with stress (that is, forces that act on the surface of an object) vary from one part of the object's surface to another, the object can undergo distortion. What are the two types of distortion? (Pick the one correct answer.)

1. Changes in the volume of the object (expansion/inflation or compression), and shear.
2. Convergence or divergence of the surface of the object, and shear.
3. Rotation of the object's orientation in space (spinning) due to torque applied to the object, and changes in the volume of the object (expansion/inflation or compression).
4. Changes in the length of the object along any particular axis or dimension (extension/elongation or contraction), and shear.

(3) Multiple Choice. What information (constraints, conditions) must we specify as part of solving the governing equations to forecast/predict the future state of a fluid? (Pick the one correct answer.)

1. The volume and shape of the fluid at some starting time.
2. The mass and velocity of the fluid at some starting time.
3. The initial (starting) state of the fluid, and the conditions that must be met on the solid and gaseous boundaries of the fluid.
4. The recent history of the fluid's behavior leading up to the current time.

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