Practice Question: Size a Detention Tank Based on Flow

---

---

Solution

Answer: C) 19 ft

Detention time:
$$ t = 4 \ hr $$
Flow into the tank:
$$ Q = \ 500 \ gpm $$

Radius of the tank:
$$ r = 20 \ ft $$
Volume of tank, where h represents the height required for water detention:

$$ V = \pi \ast \ r^2 \ast \ h $$

Volume based on flow over time:
$$ V = Q \ast \ t $$

Setting the two volumes equal:

$$ Q \ast \ t = \pi \ast \ r^2 \ast \ h $$

$$ 500 \ gpm \ast 4 \ hr \ast \frac{60 \ min}{1 \ hr} \ast \frac{1 \ ft ^ 3}{7.48 \ gal} = \pi \ast (20 \ ft) ^ 2 \ast \ h $$

Solving for h:
$$ h = 12.8 \ ft $$

To obtain the total minimum tank height, we add height of freeboard and siltation to h:

$$ h_t = 12.8 \ ft + 2 \ ft + 4 \ ft \ \approx 19\ ft $$

---