Step 1: Understanding the Concept:
Irrigation system design requires matching field slopes and soil types with specific irrigation methods to prevent erosion and achieve uniform water application.
Step 2: Detailed Explanation:
1. Furrow Irrigation Slopes:
- A minimum slope of \(0.05\%\) (Statement C) is standard to permit runoff and assist drainage, preventing stagnation.
- Contour furrows on steep land can sometimes be laid out on higher slopes, but Statement B lists a restricted limit.
2. Border Irrigation Slopes:
- Slopes in border irrigation must be chosen to control water velocity.
- On highly permeable sandy soils, slopes up to \(2\%\) (Statement D) are acceptable because rapid infiltration reduces erosion hazards.
- For heavy clay soils, border slopes must be kept flat (\(0.05\%\) to \(0.2\%\)) to facilitate slow infiltration and avoid runoff erosion. Hence, a \(3\%\) slope on clay soil (Statement E) is too steep and incorrect.
3. Consequently, Statements C and D are accurate and representative of these design principles.
Step 3: Final Answer:
The correct combination is (C) and (D) only.