Answer:
51.02 minutes
Explanation:
d = Diameter
r = Radius = [tex]\frac{d}{2}[/tex]
h = Height of pool = 0.43 cm
v = Speed of water = 1.5 m/s
A = Area = [tex]\pi r^2[/tex]
Volume flow rate is given by
[tex]Q=Av\\\Rightarrow Q=\pi 0.015^2\times 1.5\\\Rightarrow Q=0.00106\ m^3/s[/tex]
Volume of water needed is given by
[tex]V=\pi r^2h\\\Rightarrow V=\pi 1.55^2\times 0.43\\\Rightarrow V=3.2455\ m^3[/tex]
Time taken is given by
[tex]t=\frac{V}{Q}\\\Rightarrow t=\frac{3.2455}{0.00106}\\\Rightarrow t=3061.79245\times \frac{1}{60}=51.02\ min[/tex]
The time taken to fill the pool is 51.02 minutes
