The maximum effective precipitation for a basin is shown in the table below.

Question

Determine the hydrograph. The basin has the following characteristics drainage area of 27 km2 , the length of the river is 8 km and the gradient

Time (h) Precipitation (mm)

1 7

2 10

3 5

4 3

Answer 1

Hi Gabriel,

Here are Step-by-Step Hydrograph Determinations

Given Data:

1. Drainage Area (A): 27 km²
2. River Length (L): 8 km
3. Time-Precipitation Table (provided)
4. Note: Gradient value appears incomplete in your question

Solution Approach:

1. Effective Rainfall Calculation
2. Convert precipitation to effective runoff (assuming no initial losses)
3. Example for Hour 1: 7 mm → 7/1000 m × 27×10⁶ m² = 189,000 m³
4. Time of Concentration (tₐ) Estimation
5. Using Kirpich's formula (requires gradient S):
6. tₐ = 0.0195*(L^0.77)/(S^0.385)
7. [Please provide gradient to complete this calculation]
8. Unit Hydrograph Application
9. For a 1-hour unit hydrograph (typical for small basins):
10. Qₚ = (2.08×A)/tₐ (peak discharge in m³/s)
11. Tₚ = tₐ/2 + 0.6tₐ (time to peak)
12. Convolution Calculation
13. Multiply unit hydrograph ordinates by effective rainfall
14. Sum lagged hydrographs from each time interval

Key Observations:

1. The peak discharge will occur between Hours 2-3 (maximum rainfall intensity)
2. Basin response time depends heavily on the missing gradient value

Why This Matters:

Proper hydrograph analysis is crucial for:

1. Flood prediction
2. Infrastructure design
3. Watershed management

Need the Complete Solution?

I offer:

1. Step-by-Step Spreadsheet with all calculations
2. Visual Hydrograph Plotting
3. Sensitivity Analysis for different gradients

Book a session and receive:

✓ Completed Excel solver template

✓ 3 alternative methods comparison (SCS, Snyder, Rational)

✓ Gradient estimation techniques

I am available Thursday/Friday - message to schedule!

Best Regards,

Aaron