Question

A tile drainage system having a drainage coefficient of 25 mm drains an area of \(0.2\ \text{km}^2\). The average discharge from the system (in \(\text{m}^3.\text{s}^{-1}\)) is ________. (Rounded off to three decimal places)

Hint:

Convert the drainage coefficient and area into consistent SI units before finding volume per day.

Answer 1

Correct Answer: 0.058

Step 1: Convert the drainage coefficient and area to SI units.
Drainage coefficient \(DC = 25\ \text{mm/day} = 0.025\ \text{m/day}\).
Area \(A = 0.2\ \text{km}^2 = 0.2 \times 10^6\ \text{m}^2 = 200000\ \text{m}^2\).

Step 2: Find the volume drained per day.
Volume per day \(= DC \times A = 0.025 \times 200000 = 5000\ \text{m}^3/\text{day}\).

Step 3: Convert the daily volume to an average discharge in \(\text{m}^3/\text{s}\).
One day has \(86400\) seconds.
\(Q = \dfrac{5000}{86400} = 0.05787\ \text{m}^3/\text{s}\).

Final Answer:
The average discharge from the tile drain rounds to 0.058 cubic metres per second. \[ \boxed{Q \approx 0.058\ \text{m}^3/\text{s}} \]