SME
Hydraulics & Hydrology · Problem type
Time of concentration by Kirpich
Use this for “The longest flow path in a small rural watershed is 3000 ft long and falls 60 ft (slope 0.02). What is its time of concentration?”
Chart
tc(3,000) ≈ 16.7
This is an example. Type your own values to start a new problem.
tc (min)
=
0.0078
×
(
L (ft)
)
0.77
S
0.385
Formulas
tc
=
0.0078
×
L
0.77
S
0.385
16.7
=
0.0078
×
3,000^
0.77
0.02
0.385
Assumptions
•
A small rural watershed with a defined channel, the kind Kirpich fitted the rule to.
•
L is the longest flow path to the outlet; S is its fall over its length (ft per ft).
•
L in feet gives tc in minutes: the 0.0078 holds only in those units.
Step-by-step
WE KNOW
L = 3,000 ft, S = 0.02
FIND
time of concentration (tc)
Step 1 · Find time of concentration (tc)
Use tc = 0.0078 × L0.77 ÷ S0.385
A
longer
path
takes
longer
to
drain;
a
steeper
one
drains
faster,
so
S
divides.
tc
=
0.0078
×
3,000^
0.77
0.02
0.385
tc
=
0.0078
×
475.8
0.2218
tc
=
3.711
0.2218
tc = 16.7 min
Check
Put the numbers back in. Both sides should match.
16.7
=
0.0078
×
3,000^
0.77
0.02
0.385
✓
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