Question

A spherical hot air balloon is initially filled with air having 120 kPa pressure and 24 °C temperature. Initial diameter of the hot air balloon was measured to be equal to 9.905 m. Before operating balloon the operator filled the balloon with air having 120 kPa pressure and 24 °C temperature via an inlet having 1.458 m diameter. It took operator 17.108 minutes to fill balloon to its operation diameter of 16.502 m. Calculate the velocity of air supply from the pump to the balloon through the inlet. Give your answer in m/s having 3 decimal points.

Answer 1

v = 1.076 m /s

Step-by-step explanation:

Initial volume of balloon = 4/3 x 3.14 x (9.905/2)³

=508.56 m³

Final volume of balloon = 4/3 x 3.14 x (16.502/2)³

= 2351.73 m³

Increase in volume = 1843.17 m³

Cross sectional area of inlet A = 3.14 x( 1.458/2)²

A = 1.6687 m²

Volume rate of flow of air = cross sectional area x velocity of inflow

= 1 .6687 V [ V is velocity of inflow ]

Total time taken = Increase in volume / rate of flow of air

17.108 X 60 = 1843.17 / 1.6687 V

V =
`(1843.17)/(1.6687*17.108*60)`

v = 1.076 m /s