A balloon filled with helium (of density ρHe = 0.164 kg/m3 ) has a cube shape and rises through the stratosphere. Air density is given by ρ(z) = ρa exp(− gz/ RT), where ρa = 1.225 kg/m3 is the density of air at the sea level, g = 9.81 m/s^2 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 ρHe 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. 4. A balloon filled with helium (of density Pte = 0.164 kg/m) has a cube shape and rises through the strato-sphere. Air density is given by p(:) = Pa exp(-). where p. = 1.225 kg/m is the density of air at thesea level, g = 9.81 m/s is the gravitational acceleration, R = 287.06 J/kg/K is the specific gas constant ofair, and T is the air temperature, which is constant in the stratosphere and equal to 217 K (Note that thisexpression 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 PHe and its side lengthh = 30 cm remain constant for all z. The lower surface is located at z and the upper surface at z+h. Derivean expression for the buoyancy force on the balloon and compute the maximum altitude to which the balloonrises in a unit of m.hНе

Given data: Density of helium = ρHg= 0.164 kg/m3Air density is given by ρ(z) = ρa exp -gzRT =…

Answered: 4. A balloon filled with helium (of…

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 ρHe = 0.164 kg/m3 ) has a cube shape and rises through the stratosphere. Air density is given by ρ(z) = ρa exp(− gz/ RT), where ρa = 1.225 kg/m3 is the density of air at the sea level, g = 9.81 m/s^2 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 ρHe 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.

4. A balloon filled with helium (of density Pte = 0.164 kg/m) has a cube shape and rises through the strato-
sphere. Air density is given by p(:) = Pa exp(-). where p. = 1.225 kg/m is the density of air at the
sea level, g = 9.81 m/s 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 PHe 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.
h
Не

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