Chapter 16.7, Problem 43E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

A fluid has density 870 kg/m^{3} and flows with velocity **v** = z **i** + *y*^{2} **j** + *x*^{2} **k**, 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 cylinder *x*^{2} + *y*^{2} = 4, 0 ≤ *z* ≤ 1.

To determine

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

Explanation

**Given:**

The density of the fluid is

The equation of the cylinder is given by

**Formula used:**

**Calculation:**

By using the parametric representation of the cylinder, consider

Substitute

Substitute

Find

To find

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