A spherical hot-air balloon is initially filled with air at 120 kPa and 20°C with an initial diameter of 5 m. Air enters this balloon at 120 kPa and 20°C with a velocity of 3 m/s through a 1-m-diameter opening. How many minutes will it take to inflate this balloon to a 16.9-m diameter when the pressure and temperature of the air in the balloon remain the same as the air entering the balloon? The gas constant of air is R = 0.287 kPa·m3/kg·K.

27.78 s

Explanation:

Assume ideal gas, since pressure and temperature of the air inside the balloon is the same as air entering the balloon, then the volume (and its rate) stays the same.

The cross-sectional area of the hole where air enters

Hence the volume rate:

The total volume of the spherical balloon is

Hence the time it takes to fill this much at a constant rate of 3π/4 is

the working equation for the angular size is the product of the physical size and 360 degrees divided by the product of two pi and distance from earth. the minimum size would be 0.559 degrees while the maximum size would be 0.49 degrees. 

a lot of it means it can be "burned" for energy and sold at one price. if it is scarce, the price will go up