Respuesta :
Explanation:
At temperature is [tex]33^{\circ} C[/tex] and relative humidity is 86% therefore, the humidity ratio is 0.0223 and the specific volume is 14.289
At temperature is [tex]33^{\circ} C[/tex] and Relative humidity is 40% therefore, the humidity ratio is 0.0066 and the specific volume is 13.535.
To calculate the mass of air can be calculated as follows:
[tex]\begin{aligned}m _{1} &=\frac{ v }{ v }(1- w ) \\&=\frac{1 \times 10^{5}}{13.535}(1-0.0066) \\&=7339.49 lb / min \\v _{ a } &=\frac{ m _{1} v }{(1- w )} \\v _{ a } &=\frac{7339.49 \times 14.289}{(1-0.0223)} \\v _{ a } &=107266.0 ft ^{3} / min\end{aligned}[/tex]
Now , we going to calculate the volume,
[tex]\begin{aligned}m _{ w } &=\frac{ v _{ a }}{ v _{ a }} w _{ a }-\frac{ v _{ i }}{ v _{ i }} w _{ i } \\&=\frac{107266.0}{14.289} \times 0.0223-\frac{100000}{13.535} \times 0.0066 \\&=118.64 lb / min\end{aligned}[/tex]
The time which is required to fill the cistern can be calculated as follows:
[tex]Time \(=\frac{\text { cistern volume }}{\text { removal water perminute volume }}\)[/tex]
Now, putting the value in above formula we get,
[tex]\(\frac{\left(15 \times 10^{3} L\right) \times\left(0.0353147 ft ^{3} / L \right)}{(118.641 b / min ) \times\left(\frac{1}{62.41 lb / ft ^{3}}\right)}\)\\\(=279.09\) minutes\\\(=4.65\) hours.[/tex]
Therefore, the hours required to fill the cistern is 4.65 hours.
