Figure 1. A rubber balloon for atmospheric testing is launched. Engineer the bal

Question

Figure 1. A rubber balloon for atmospheric testing is launched. Engineer the balloon in such a way that it reaches a height of 15 km. A balloon for atmospheric testing is to be launched. Your engineering task is to make sure that the balloon reaches the correct height. Assume that the coefficient C that describes the tension of the rubber balloon (C) equals C = 30000 Pa m^3 (equation in figure lb). The temperature change with altitude can be assumed linear with a coefficient of -6 degree C. The tension in the balloon is determined by the elasticity of the rubber sheet and the thickness of the membrane which decreases as the radius of the balloon increases. Also the elasticity of rubber varies with its elongation. Derive an equation for the mass density of air as a function of the height using the pressure and temperature equations. What is the air density, temperature and pressure at an altitude of 15 km?| What should be the radius of the balloon at an altitude of 15 km when the balloon with measurement equipment has a mass of 10 kg and is in equilibrium?

Explanation / Answer

1)     mass density of air = Po(1 - Lh/To)gM/RL/gh

=> air density = 1.1225 kg/m3

=> temperature =   300 K

=> pressure =    101320 Pa

2)   Here, 4/3 * 3.14 * r3 * 1.1225   =   10

=>    radius of balloon , r = 1.286 m

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