A cylinder of diameter S, of height h, contains pure gas with equation PV = nRT at constant temperature T_0. The z axis is directed upwards and the gravitational field is assumed to be uniform. 1) Using the fundamental principle of hydrostatic statistics, show that dp = -pgdz where p = p (z) is the gas pressure at height z. 2) If P_0 is the gas pressure at the foot of the pole, calculate the pressure p (z) at height z. 3) In the case of wind (M = 29 g / mol: R = 8.31J/ mol.k) at temperature T_0 = 300K, calculate the height of the poles necessary to observe the change in pressure (pressure at the threshold) at 5% .

A cylinder of diameter S, of height h, contains pure gas with equation PV = nRT at constant temperature T_0. The z axis is directed upwards and the gravitational field is assumed to be uniform. 1) Using the fundamental principle of hydrostatic statistics, show that dp = -pgdz where p = p (z) is the gas pressure at height z. 2) If P_0 is the gas pressure at the foot of the pole, calculate the pressure p (z) at height z. 3) In the case of wind (M = 29 g / mol: R = 8.31J/ mol.k) at temperature T_0 = 300K, calculate the height of the poles necessary to observe the change in pressure (pressure at the threshold) at 5% .

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter15: Fluid Mechanics

Section: Chapter Questions

Problem 29P: How many cubic meters of helium are required to lift a balloon with a 400-kg payload to a height of...

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