SME
Hydraulics & Hydrology
Stormwater design
Use this for “What size concrete storm sewer (n = 0.013) on a 0.005 slope carries 1.667 m³/s flowing full?”
Diagram
Full
by
Manning:
D
=
(3.208Qn ÷ √S)
3
ᐟ
8
=
0.994
m
(dashed),
so
the
next
size
up
is
laid.
Full,
V
=
Q
A
=
1.93
m/s,
above
about
0.9
m/s,
so
solids
keep
moving.
This is an example. Type your own values to start a new problem.
D (mm)
=
3.208
×
Q (m³/s)
×
S
3
8
V
Full-flow speed
calculated · m/s
Formulas
D
=
(3.208 ×
Q
×
n
÷ √
S
)
3
8
0.9937
=
(3.208 × 1.667 × 0.013 ÷
√
0.005
)
3
8
V
=
4
×
Q
π ×
D
2
2.1497
=
4
×
1.667
π ×
0.9937
2
Formulas are worked in m. The step-by-step shows the conversions.
Assumptions
•
The pipe runs just full, not under pressure; Manning’s equation in SI, with Q in m³/s and D in m.
•
Lay the next size made at least D (300, 375, 450 … 3600 mm); the picture picks it.
•
Full, the speed V should stay above about 0.9 m/s so the flow carries solids along.
•
n is about 0.013 for concrete pipe and 0.010 for plastic.
Step-by-step
WE KNOW
Q = 1.667 m³/s, n = 0.013, S = 0.005
FIND
diameter needed (D), full-flow speed (V)
Step 1 · Find diameter needed (D)
Use D = (3.208 × Q × n ÷ √S)3/8
Manning’s
equation
for
a
round
pipe
running
full,
solved
for
D
.
D
=
(3.208 × 1.667 × 0.013 ÷
√
0.005
)
3
8
D
=
(3.208 × 1.667 ×
0.013
0.07071
)
3
8
D
=
(5.348 ×
0.013
0.07071
)
3
8
D
=
(
0.06952
0.07071
)
3
8
D
=
0.9832
3
8
D
=
0.9937
m
Step 2 · Find full-flow speed (V)
Use V = 4 × Q ÷ (π × D²)
The flow over the full circle’s area; above about 0.9 m/s the pipe keeps itself clean.
V
=
4
×
1.667
π ×
0.99365
2
V
=
4
×
1.667
0.9873 × π
V
=
4
×
1.667
3.102
V
=
6.668
3.102
V
=
2.1497
m/s
Step 3 · Convert the answers
Change each answer back to the unit you chose.
D = 0.9937 m = 993.65499 mm (1 m = 1000 mm)
Check
Put the numbers back in. Both sides should match.
0.99365
=
(3.208 × 1.667 × 0.013 ÷
√
0.005
)
3
8
✓
2.1497
=
4
×
1.667
π ×
0.99365
2
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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