Solution: Calculating Watershed Drainage Coefficient

The drainage coefficient represents the average depth of runoff from a watershed. Here, we calculate this depth in centimeters, assuming it relates to a 24-hour period (daily runoff).

Given Information

• Watershed Area, $A = 16.95 \text{ km}^2$
• Average Drainage Rate, $Q = 2.8 \text{ m}^3/\text{s}$

Step 1: Convert Area Units

Convert the watershed area from square kilometers ($\text{km}^2$) to square meters ($\text{m}^2$) for consistent calculations.

$A = 16.95 \text{ km}^2 \times \left( \frac{1000 \text{ m}}{1 \text{ km}} \right)^2 = 16.95 \times 10^6 \text{ m}^2$

Step 2: Define Time Period

Assume the drainage coefficient 'in cm' refers to the average runoff depth over a standard period, typically a day.

Time, $T = 1 \text{ day} = 24 \text{ hours} \times 3600 \text{ seconds/hour} = 86400 \text{ seconds}$

Step 3: Calculate Daily Runoff Volume

Calculate the total volume of water drained over the assumed 1-day period using the given average flow rate.

Volume, $V = Q \times T$ $V = 2.8 \text{ m}^3/\text{s} \times 86400 \text{ s} = 241920 \text{ m}^3$

Step 4: Determine Average Depth in Meters

Find the average depth of this volume spread across the watershed area.

Average Depth (meters), $d_m = \frac{V}{A}$ $d_m = \frac{241920 \text{ m}^3}{16.95 \times 10^6 \text{ m}^2} \approx 0.014272566 \text{ m}$

Step 5: Convert Depth to Centimeters and Round

Convert the average depth from meters to centimeters and round the final value to two decimal places.

Drainage Coefficient (cm), $D_{cm} = d_m \times 100 \text{ cm/m}$ $D_{cm} = 0.014272566 \text{ m} \times 100 \text{ cm/m} \approx 1.4272566 \text{ cm}$

Rounding to two decimal places gives 1.43 cm.