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

Answer:

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.

Step-by-step 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

$V=\frac{4}{3}\pr r^3$

$V=\frac{4}{3}\times 3.14\times (5 ft)^3$

Specific volume of the air in balloon = S

$S=\frac{V}{m}=\frac{\frac{4}{3}\times 3.14\times (5 ft)^3}{35 lbm}$

$S=14.96 ft^3/lbm$

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]

$W=35 lbm\times 32.174 lbm ft/s^2$

$W=1,126.09 lbf$

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