5. what is the detention time (in minutes) for a tank with a diameter of 30 feet and a depth of 20 feet with…

Explanation:

Step1: Calculate tank volume

The tank is cylindrical. The volume formula for a cylinder is $V=\pi r^{2}h$. Given diameter $d = 30$ feet, so radius $r=\frac{d}{2}=15$ feet and height $h = 20$ feet. Then $V=\pi\times(15)^{2}\times20=\pi\times225\times20 = 4500\pi$ cubic - feet. Since $1$ gallon $= 0.133681$ cubic - feet, the volume in gallons is $V_{gal}=\frac{4500\pi}{0.133681}\approx\frac{4500\times3.14159}{0.133681}\approx106028.7$ gallons.

Step2: Convert flow rate to gallons per minute

The flow rate is $2$ MGD (million gallons per day). There are $24\times60 = 1440$ minutes in a day. So the flow rate $Q$ in gallons per minute is $Q=\frac{2\times10^{6}}{1440}\approx1388.89$ gallons per minute.

Step3: Calculate detention time

The detention time $t$ is given by the formula $t=\frac{V}{Q}$. Substituting the values of $V_{gal}$ and $Q$ we found above, $t=\frac{106028.7}{1388.89}\approx76.3$ minutes.

Answer:

$76.3$ minutes