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Fluid Mechanics | 2nd Edition | ISBN: 9780071284219 | Authors: Yunus A. Cengel, John M. Cimbala
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Solved: The density of atmospheric air varies with

Chapter 2, Problem 15P

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QUESTION:

Problem 15P

 The density of atmospheric air varies with elevation, decreasing with increasing altitude, (a) Using the data given in the table, obtain a relation for the variation of density with elevation, and calculate the density at an elevation of 7000 m. (b) Calculate the mass of the atmosphere using the correlation you obtained. Assume the earth to be a perfect sphere with a radius of 6377 km, and take the thickness of the atmosphere to be 25 km.

r, km

ρ, kg/m3

6377

1.225

6378

1.112

6379

1.007

6380

0.9093

6381

0.8194

6382

0.7364

6383

0.6601

6385

0.5258

6387

0.4135

6392

0.1948

6397

0.08891

6402

0.04008

Vapor Pressure and Cavitation

Questions & Answers

QUESTION:

Problem 15P

 The density of atmospheric air varies with elevation, decreasing with increasing altitude, (a) Using the data given in the table, obtain a relation for the variation of density with elevation, and calculate the density at an elevation of 7000 m. (b) Calculate the mass of the atmosphere using the correlation you obtained. Assume the earth to be a perfect sphere with a radius of 6377 km, and take the thickness of the atmosphere to be 25 km.

r, km

ρ, kg/m3

6377

1.225

6378

1.112

6379

1.007

6380

0.9093

6381

0.8194

6382

0.7364

6383

0.6601

6385

0.5258

6387

0.4135

6392

0.1948

6397

0.08891

6402

0.04008

Vapor Pressure and Cavitation

ANSWER:

Step 1 of 6

Density decreases exponentially with height as

 ….(1)

That is the approximate model that follows density decrement with height

Here

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