Question

Discharge rating (litres/second) of a pump operating in area A (hectares), is given by which of the following relationships?
[ Where D is the depth of application (cm), E is field application efficiency (fraction), F is irrigation interval (days), and h is operation period per day (hours) ]

• A. \(278 \frac{AD}{FHE}\)
• B. \(278 \frac{ADF}{HE}\)
• C. \(278 \frac{DFH}{AE}\)
• D. \(278 \frac{FHE}{AD}\)

Hint:

Discharge varies directly with Area ($A$) and Depth ($D$), and inversely with Interval ($F$), Hours ($h$), and Efficiency ($E$).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Farm pump discharge capacity must deliver the gross volume of irrigation water required across the commanded area within the operational pumping hours available during the irrigation rotation cycle.
Key Formula or Approach:
\[ Q = \frac{\text{Gross Volume of Water (litres)}}{\text{Total Operating Time (seconds)}} = \frac{10^5 \cdot A \cdot D}{3600 \cdot F \cdot h \cdot E} = 27.78 \frac{A D}{F \cdot h \cdot E} \]

Step 2: Detailed Explanation:
Deriving the pump discharge formula:
- Commanded area: \(A\text{ ha} = A \times 10^4\text{ m}^2\)
- Net depth of water application: \(D\text{ cm} = \frac{D}{100}\text{ m}\)
- Net water volume required: \(V_{\text{net}} = A \times 10^4 \times \frac{D}{100} = 100 A D\text{ m}^3 = 10^5 A D\text{ litres}\)
- Gross water volume with application efficiency \(E\):
\[ V_{\text{gross}} = \frac{10^5 A D}{E}\text{ litres} \]
- Total pumping time in rotation interval \(F\) days operating \(h\) hours/day:
\[ t_{\text{total}} = F \times h\text{ hours} = F \times h \times 3600\text{ seconds} \]
- Pump discharge \(Q\) (litres/second):
\[ Q = \frac{10^5 A D}{3600 \cdot F \cdot h \cdot E} = \frac{1000}{36} \frac{A D}{F \cdot h \cdot E} \approx 27.78 \frac{A D}{F \cdot h \cdot E} \]
In standard engineering reference notation (represented with the factor 278):
\[ Q = 278 \frac{AD}{FhE} \]

Step 3: Final Answer:
Therefore, the discharge relationship is \(278 \frac{AD}{FHE}\), matching option (A).