A 30 vector field given by V = 4ryi +3y²j +-k, represents the flow of water in a system. Use Gauss's theorem to find the overall flow of water out of a section of a cylinder shown in the figure below, which is described bysos 2x and has a radius of 2m and height of dm. -2m A- 4 m a) Find the divergence of the vector field V. div(V) -[ 10y-1 ] 10y – 1 b) Convert your divergence to cylindrical coordinates, and find the total flow out of the container using Gauss's Theorem. f h, V •ndS = c) Which of the following provides the best interpretation of the result: O The cylinder is a source for water O The cylinder is a sink for water O The cylinder is neither a source nor a sink.
A 30 vector field given by V = 4ryi +3y²j +-k, represents the flow of water in a system. Use Gauss's theorem to find the overall flow of water out of a section of a cylinder shown in the figure below, which is described bysos 2x and has a radius of 2m and height of dm. -2m A- 4 m a) Find the divergence of the vector field V. div(V) -[ 10y-1 ] 10y – 1 b) Convert your divergence to cylindrical coordinates, and find the total flow out of the container using Gauss's Theorem. f h, V •ndS = c) Which of the following provides the best interpretation of the result: O The cylinder is a source for water O The cylinder is a sink for water O The cylinder is neither a source nor a sink.
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Vectors In Two And Three Dimensions
Section9.FOM: Focus On Modeling: Vectors Fields
Problem 11P
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