## Unit hydrograph

In the introduction section we discussed some basics of what is hydrograph and hydrologic routing. Check out Hydrographs - Click Here Taking our discussion further, we'll discuss unit hydrograph now. Unit Hydrograph is the hydrograph of one inch of**excess rainfall**distributed uniformly over the drainage area for a given duration 'D'. This is known as Unit Hydrograph for duration D. If we need to compute the hydrograph for 2 or 3 inches of rainfall excess over duration D, we simply multiply each ordinate of the unit hydrograph with 2 or 3 respectively.

Example: Given the following 2-hour unit hydrograph, compute the discharge hydrograph for the rain that occurred over 4 hour duration as:

1st hour:0.6 in,

2nd hour:0.6 in,

3rd hour:1.0 in,

4th hour:1.0 in.

Time (hr) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Unit Hydrograph (cfs) | 0 | 20 | 45 | 60 | 46 | 34 | 21 | 14 | 9 | 4 | 0 | 0 | 0 |

**Solution:**

Following table provides the self explanatory solution. The first 2 hour had 1.2 inch of total excess rainfall, so we multiply each UH ordinate by 1.2 and second 2 hour duration had 2.0 inch of total excess rainfall, so we multiply each UH ordinate by 2.0 for the second half.

We delayed the second 2 hour discharge hydrograph by 2 hour and then added the ordinates of it with the ordinates of first 2 hour discharge hydrograph. The combined value provides the total discharge hydrograph. This is possible due to assumption of linearity or sometimes known as superposition principle.

Time UH 1st 2nd Total (hr) (cfs) 2-hour 2-hour (cfs) 0 0 0 0 1 20 24 24 2 45 54 0 54 3 60 72 40 112 4 46 55.2 90 145.2 5 34 40.8 120 160.8 6 21 25.2 92 117.2 7 14 16.8 68 84.8 8 9 10.8 42 52.8 9 4 4.8 28 32.8 10 0 0 18 18 11 0 0 8 8 12 0 0 0 0