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A balloon is surrounded by a tank of liquid at negative pressure and is con- nected to the atmosphere by a tube of length L and cross-sectional area A (Fig. 7.25). The pressure inside the balloon p oscillates above and below atmospheric pressure causing small changes in the balloon volume V. The elasticity of the balloon is characterized by its compliance C, defined by Ap = AV/C (a) Derive a second-order differential equation for AV(t), assuming that (i) the pressure differential along the tube accelerates the air in the tube and is not used to overcome entrance, exit, or tube losses; and (ii) the air density p is constant. From the equation, show that the natural frequency of the system is JA/pLC. Atmosphere Length = L; Cross-sectional area = A Air at pressure p Liquid Balloon Figure 7.25

A balloon is surrounded by a tank of liquid at negative pressure and is con- nected to the atmosphere by a tube of length L and cross-sectional area A (Fig. 7.25). The pressure inside the balloon p oscillates above and below atmospheric pressure causing small changes in the balloon volume V. The elasticity of the balloon is characterized by its compliance C, defined by Ap = AV/C (a) Derive a second-order differential equation for AV(t), assuming that (i) the pressure differential along the tube accelerates the air in the tube and is not used to overcome entrance, exit, or tube losses; and (ii) the air density p is constant. From the equation, show that the natural frequency of the system is JA/pLC. Atmosphere Length = L; Cross-sectional area = A Air at pressure p Liquid Balloon Figure 7.25

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 is surrounded by a tank of liquid at negative pressure and is con- nected to the atmosphere by a tube of length L and cross-sectional area A (Fig. 7.25). The pressure inside the balloon p oscillates above and below atmospheric pressure causing small changes in the balloon volume V. The elasticity of the balloon is characterized by its compliance C, defined by Ap = AV/C (a) Derive a second-order differential equation for AV(t), assuming that (i) the pressure differential along the tube accelerates the air in the tube and is not used to overcome entrance, exit, or tube losses; and (ii) the air density p is constant. From the equation, show that the natural frequency of the system is JA/pLC.
Transcribed Image Text:A balloon is surrounded by a tank of liquid at negative pressure and is con- nected to the atmosphere by a tube of length L and cross-sectional area A (Fig. 7.25). The pressure inside the balloon p oscillates above and below atmospheric pressure causing small changes in the balloon volume V. The elasticity of the balloon is characterized by its compliance C, defined by Ap = AV/C (a) Derive a second-order differential equation for AV(t), assuming that (i) the pressure differential along the tube accelerates the air in the tube and is not used to overcome entrance, exit, or tube losses; and (ii) the air density p is constant. From the equation, show that the natural frequency of the system is JA/pLC.
Atmosphere Length = L; Cross-sectional area = A Air at pressure p Liquid Balloon Figure 7.25
Transcribed Image Text:Atmosphere Length = L; Cross-sectional area = A Air at pressure p Liquid Balloon Figure 7.25
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