SME
Hydraulics & Hydrology · Problem type
Detention storage from the two peaks
Use this for “A pond takes an inflow peak of 3 m³/s and may let out only 1.2 m³/s. Both hydrographs last 2 h. How much must it store?”
Diagram
The inflow triangle holds ½tbQᵢ and the outflow ½tbQₒ; the shaded difference is stored: V = ½tb(Qᵢ − Qₒ) = ½ × 7,200 × 1 × (3 − 1.2) = 6,480 m³.
This is an example. Type your own values to start a new problem.
V (m³)
=
0.5
×
tb (h)
×
(
Qᵢ (m³/s)
−
Qₒ (m³/s)
)
Formulas
V
=
0.5
×
tb
×
(Qᵢ
−
Qₒ)
6,480 = 0.5 × 7,200 × (3 − 1.2)
Formulas are worked in s. The step-by-step shows the conversions.
Assumptions
•
The inflow and outflow hydrographs are triangles on the same base time tb.
•
The outflow peaks where it meets the inflow’s falling limb; the storage is the area between them.
•
Qₒ is the most the outlet may release, often the peak before development.
Step-by-step
WE KNOW
Qᵢ = 3 m³/s, Qₒ = 1.2 m³/s, tb = 2 h
FIND
storage volume (V)
Step 1 · Convert to the formula’s units
The formulas don’t work directly in the units you chose, so convert first (to s).
tb = 2 h = 7,200 s (1 h = 3600 s)
Step 2 · Find storage volume (V)
Use V = 0.5 × tb × (Qᵢ − Qₒ)
The two triangles share their base, so the area between them is half the base times the gap between the peaks.
V
=
0.5
×
7,200
×
(3
−
1.2)
V
=
0.5
×
7,200
×
1.8
V
=
3,600
×
1.8
V
=
6,480
m³
Check
Put the numbers back in. Both sides should match.
6,480 = 0.5 × 7,200 × (3 − 1.2) ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.