Question

When \(\Delta\) (delta) is in cm, B (base period) is in days and D is in ha cumec\(^{-1}\), the correct relation is:

• A. \(\Delta = \dfrac{864\,B}{D}\) (cm)
• B. \(\Delta = \dfrac{864\,D}{B}\) (cm)
• C. \(\Delta = \dfrac{8640\,B}{D}\) (cm)
• D. \(\Delta = \dfrac{86.4\,B}{D}\) (cm)

Hint:

Start from the fact that 1 cumec running for 1 day covers 1 hectare to a depth of 8.64 metres, then convert to centimetres.

Answer 1

The Correct Option is A

This question is about the standard irrigation relation connecting delta, base period and duty, just with the units changed to centimetres for delta.

1. \(\Delta = 864B/D\) (cm): this comes from the fact that a flow of 1 cubic metre per second for one full day delivers 86400 cubic metres of water, which spread over 1 hectare (10000 square metres) gives a depth of 8.64 metres, so in centimetres that constant becomes 864, matching this option.
2. \(\Delta = 864D/B\) (cm): wrong, this inverts B and D, delta should grow with a longer base period B and shrink with a bigger duty D, not the other way round.
3. \(\Delta = 8640B/D\) (cm): wrong, this constant is ten times too big compared with the correct 864.
4. \(\Delta = 86.4B/D\) (cm): wrong, this is only ten times the metre based constant of 8.64, but converting metres to centimetres needs a factor of 100, not 10.

Working from first principles, 1 cumec-day over 1 hectare gives 8.64 m depth, and 8.64 m equals 864 cm, so the constant in the centimetre form of the equation must be 864.

Let's summarize:

• The base relation is \(\Delta(\text{m}) = 8.64B/D\), derived from unit conversion of cumec-days to hectare-metres.
• Switching delta to centimetres multiplies the constant by 100, from 8.64 to 864.

So the correct relation is \(\boxed{\Delta = 864B/D}\) in centimetres, option 1.