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.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
Question
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.
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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