Question

A spherical balloon holding 35 lbm of air on earth has a diameter of 10 ft. Determine (a) the specific volume, in unit ft3/lbm, and (b) the weight, in lbf, of the air within the balloon.

Answer 1

a) Specific volume of the air in balloon is
`14.96 ft^3/lbm`

b)The weight of the air within the balloon is 1,126.09 lbf.

Explanation:

Mass of air, m = 35 lbm

Volume of the air = V

Diameter of balloon = d = 10 ft

radius of the balloon = r= 0.5 d = 5 ft

Volume of balloon = V

`V=(4)/(3)\pr r^3`

`V=(4)/(3)* 3.14* (5 ft)^3`

Specific volume of the air in balloon = S

`S=(V)/(m)=((4)/(3)* 3.14* (5 ft)^3)/(35 lbm)`

`S=14.96 ft^3/lbm`

Specific volume of the air in balloon is
`14.96 ft^3/lbm`

`lbf=32.174 lbm ft/s^2`

Weight of the air = W

Acceleration due to gravity =
`32.174 lbm ft/s^2`

Weight = m\times g[/tex]

`W=35 lbm* 32.174 lbm ft/s^2`

`W=1,126.09 lbf`

The weight of the air within the balloon is 1,126.09 lbf.