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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.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Show and explain all steps, especially the orientation of n. Do not use Stoke's Theorem or Divergance Theorem, as those are from the next chapter. 

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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