A storm with a duration of about 24 hours resultsin the following hydrograph at a gaging station on a river. The flow was 52 cubic meters per second (cms) before the rain began. The drainage area above the gaging station is 1,450 square kilometers. Use the observed hydrograph to develop a 24-hour rainfall duration unit hydrograph for this watershed. Time 0 6 12 18 24 30 36 42 48 54 60 66 72 78 84
(Hours)
Flow 52 52 55 56 97 176 349 450 442 370 328 307 280 259 238
(m3/s)
Time 90 66 102 108 114 120 126 132 138 144 155 156 162 168 176
(Hours)
(m3/s) 214 193 173 145 135 124 114 107 97 86 79 66 62 58 52

attached below

Explanation:

Given data:

Gaged flow = 52 m^3 / sec

Depth covering drainage area = 1450 km^2

Develop a 24-hour rainfall duration unit hydrograph for the watershed using observed hydorgraph

Runoff flow = gaged flow - base flows

                   = 52 - 52 = 0 m^3/sec

For 18 hours time duration

Direct runoff volume ( Vr ) = ∑ ( QΔt1 )

where Δt = 6

           ∑Q = 3666 m^3/sec

hence Vr = Δt * ∑Q  = 79185600 m^3

Next we will convert the Direct runoff volume to its equivalent depth covering the drainage area

= Vr / drainage area depth

= 79185600 / 1450000000 = 5.46 cm

Next we will find the unit hydrograph flows by applying the relation below

where 14m^3/sec =

input value back to the above relation

Attached below is The remaining part of the solution  tabulated below

and A graph of the unit hydorgraph for the given watershed

Note :

Base  flow total = 1560

UH total = 671.30

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explanation: