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?40E atmospheric pressure (force per unit area) on a

Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider ISBN: 9780321747730 43

Solution for problem 40E Chapter 2.2

Fundamentals of Differential Equations | 8th Edition

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Fundamentals of Differential Equations | 8th Edition | ISBN: 9780321747730 | Authors: R. Kent Nagle, Edward B. Saff, Arthur David Snider

Fundamentals of Differential Equations | 8th Edition

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Problem 40E

40E Problem

The atmospheric pressure (force per unit area) on a surface at an altitude z is due to the weight of the column of air situated above the surface. Therefore, the difference in air pressure p between the top and bottom of a cylindrical volume element of height _z and cross-section area A equals the weight of the air enclosed (density p times volume  times gravity g), per unit area:

Let

(a) Derive the equation

(b) If the temperature also varies with altitude T= T(z) , derive the solution

(c) Suppose an engineer measures the barometric pressure at the top of a building to be 99,000 Pa (pascals), and 101,000 Pa at the base (z = z0). If the absolute temperature varies as  determine the height of the building. Take R =8.31 N-m mol-K, M = 0.029 kg mol, and g = 9.8 m sec2. (An amusing story concerning this problem can be found at http://www.snopes.com/college/exam/ barometer.asp)

Step-by-Step Solution:
Step 1 of 3

Wednesday, March 2, 2016 11:20 AM Multivariable Calc (MATH 2204) Page 1 Multivariable Calc (MATH 2204) Page 2 Multivariable Calc (MATH 2204) Page 3 Multivariable Calc (MATH 2204) Page 4 Multivariable Calc (MATH 2204) Page 5 Multivariable Calc (MATH 2204) Page 6 Multivariable Calc (MATH 2204) Page 7 Multivariable Calc (MATH 2204) Page 8 Multivariable Calc (MATH 2204) Page 9

Step 2 of 3

Chapter 2.2, Problem 40E is Solved
Step 3 of 3

Textbook: Fundamentals of Differential Equations
Edition: 8
Author: R. Kent Nagle, Edward B. Saff, Arthur David Snider
ISBN: 9780321747730

Since the solution to 40E from 2.2 chapter was answered, more than 288 students have viewed the full step-by-step answer. Fundamentals of Differential Equations was written by and is associated to the ISBN: 9780321747730. This full solution covers the following key subjects: air, pressure, area, times, varies. This expansive textbook survival guide covers 67 chapters, and 2118 solutions. This textbook survival guide was created for the textbook: Fundamentals of Differential Equations , edition: 8. The answer to “?40E atmospheric pressure (force per unit area) on a surface at an altitude z is due to the weight of the column of air situated above the surface. Therefore, the difference in air pressure p between the top and bottom of a cylindrical volume element of height _z and cross-section area A equals the weight of the air enclosed (density p times volume times gravity g), per unit area: Let (a) Derive the equation (b) If the temperature also varies with altitude T= T(z) , derive the solution (c) Suppose an engineer measures the barometric pressure at the top of a building to be 99,000 Pa (pascals), and 101,000 Pa at the base (z = z0). If the absolute temperature varies as determine the height of the building. Take R =8.31 N-m mol-K, M = 0.029 kg mol, and g = 9.8 m sec2. (An amusing story concerning this problem can be found at http://www.snopes.com/college/exam/ barometer.asp)” is broken down into a number of easy to follow steps, and 156 words. The full step-by-step solution to problem: 40E from chapter: 2.2 was answered by , our top Calculus solution expert on 07/11/17, 04:37AM.

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