Chapter 16.7, Problem 44E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Seawater has density 1025 kg/m^{3} and flows in a velocity field **v** = y **i** + x **j**, where .*x*, *y*, and *z* are measured in meters and the components of **v** in meters per second. Find the rate of flow outward through the hemisphere *x*^{2} + *y*^{2} + *z*^{2} = 9, z ≥ 0.

To determine

**To find:** The rate of flow outward through the hemisphere

Explanation

**Given:**

Density is

**Formula used:**

By using the spherical coordinates to parameterize the hemisphere, consider

Find

Substitute

Find

Substitute

Find

Find

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