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14. The cross sections of a straight canal are rectangles 40 feet wide and 10 feet high. Set up a coordinate system with the z axis vertical and the y axis running down the center of the canal bottom. Suppose the canal is full of water flowing with velocity v(x, y, z) = z(400 - x²)j where time is measured in minutes. Calculate the rate of flow of mass through a cross section perpendicular to the y axis. The mass density of water is approximately 1.95 slugs per cubic foot.

14. The cross sections of a straight canal are rectangles 40 feet wide and 10 feet high. Set up a coordinate system with the z axis vertical and the y axis running down the center of the canal bottom. Suppose the canal is full of water flowing with velocity v(x, y, z) = z(400 - x²)j where time is measured in minutes. Calculate the rate of flow of mass through a cross section perpendicular to the y axis. The mass density of water is approximately 1.95 slugs per cubic foot.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Practice problem taken from Denny Gulick, Robert Ellis - Calculus With Concepts in Calculus. Sixth-Cengage Learning, chapter 15.6 - Integrals over Oriented Surfaces.
Please show and explain ALL steps; I'm trying to practice for an exam and need help understanding this. Do not use Stokes Theorem, or Divergence Theorem, as that's not covered until the following 2 chapters.

14. The cross sections of a straight canal are rectangles 40 feet wide and 10 feet high. Set up a coordinate system with the z axis vertical and the y axis running down the center of the canal bottom. Suppose the canal is full of water flowing with velocity v(x, y, z) = z(400 - x²)j where time is measured in minutes. Calculate the rate of flow of mass through a cross section perpendicular to the y axis. The mass density of water is approximately 1.95 slugs per cubic foot.
Transcribed Image Text:14. The cross sections of a straight canal are rectangles 40 feet wide and 10 feet high. Set up a coordinate system with the z axis vertical and the y axis running down the center of the canal bottom. Suppose the canal is full of water flowing with velocity v(x, y, z) = z(400 - x²)j where time is measured in minutes. Calculate the rate of flow of mass through a cross section perpendicular to the y axis. The mass density of water is approximately 1.95 slugs per cubic foot.
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