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A balloon filled with helium (of density PHe = 0.164 kg/m³) has a cube shape and rises through the strato- sphere. Air density is given by p(z) = Pa exp(-9), where pa = 1.225 kg/m³ is the density of air at the sea level, g = 9.81 m/s² is the gravitational acceleration, R = 287.06 J/kg/K is the specific gas constant of air, and T is the air temperature, which is constant in the stratosphere and equal to 217 K (Note that this expression for the atmospheric density is strictly correct only in the isothermal region of the stratosphere. However, please use it for solution to this problem). This balloon is designed so that He and its side length h = 30 cm remain constant for all z. The lower surface is located at z and the upper surface at z+h. Derive an expression for the buoyancy force on the balloon and compute the maximum altitude to which the balloon rises in a unit of m. I h He 9

A balloon filled with helium (of density PHe = 0.164 kg/m³) has a cube shape and rises through the strato- sphere. Air density is given by p(z) = Pa exp(-9), where pa = 1.225 kg/m³ is the density of air at the sea level, g = 9.81 m/s² is the gravitational acceleration, R = 287.06 J/kg/K is the specific gas constant of air, and T is the air temperature, which is constant in the stratosphere and equal to 217 K (Note that this expression for the atmospheric density is strictly correct only in the isothermal region of the stratosphere. However, please use it for solution to this problem). This balloon is designed so that He and its side length h = 30 cm remain constant for all z. The lower surface is located at z and the upper surface at z+h. Derive an expression for the buoyancy force on the balloon and compute the maximum altitude to which the balloon rises in a unit of m. I h He 9

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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A balloon filled with helium (of density PHe = 0.164 kg/m³) has a cube shape and rises through the strato- sphere. Air density is given by p(z) = Pa exp(-9), where pa = 1.225 kg/m³ is the density of air at the sea level, g = 9.81 m/s² is the gravitational acceleration, R = 287.06 J/kg/K is the specific gas constant of air, and T is the air temperature, which is constant in the stratosphere and equal to 217 K (Note that this expression for the atmospheric density is strictly correct only in the isothermal region of the stratosphere. However, please use it for solution to this problem). This balloon is designed so that He and its side length h = 30 cm remain constant for all z. The lower surface is located at z and the upper surface at z+h. Derive an expression for the buoyancy force on the balloon and compute the maximum altitude to which the balloon rises in a unit of m. I h He 9
Transcribed Image Text:A balloon filled with helium (of density PHe = 0.164 kg/m³) has a cube shape and rises through the strato- sphere. Air density is given by p(z) = Pa exp(-9), where pa = 1.225 kg/m³ is the density of air at the sea level, g = 9.81 m/s² is the gravitational acceleration, R = 287.06 J/kg/K is the specific gas constant of air, and T is the air temperature, which is constant in the stratosphere and equal to 217 K (Note that this expression for the atmospheric density is strictly correct only in the isothermal region of the stratosphere. However, please use it for solution to this problem). This balloon is designed so that He and its side length h = 30 cm remain constant for all z. The lower surface is located at z and the upper surface at z+h. Derive an expression for the buoyancy force on the balloon and compute the maximum altitude to which the balloon rises in a unit of m. I h He 9
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