Hydraulics of water impounding behind contour bunds:
On a sloping land with slope
\(S\) (fraction), the horizontal distance between bunds \(\text{HI} = \frac{\text{VI}}{S}\). The volume of excess rainfall (\(R\)) falling on a 1-meter wide strip between consecutive bunds is: \[V_{\text{rain}} = \text{HI} \times 1 \times R = \frac{\text{VI}}{S} \times R\]
The impounded water behind the bund forms a triangular wedge of depth
\(h\) at the bund face and spreading uphill to a length \(L = \frac{h}{S}\). The storage volume of this triangular wedge per 1-meter width is: \[V_{\text{stored}} = \frac{1}{2} \times h \times L \times 1 = \frac{1}{2} \frac{h^2}{S}\]
Equating stored volume to excess rainfall volume:
\[\frac{1}{2} \frac{h^2}{S} = \frac{\text{VI}}{S} \times R \implies h^2 = 2 \cdot \text{VI} \cdot R\]
\[h = \sqrt{2 \cdot \text{VI} \cdot R}\]
Given
\(\text{VI} = 2\text{ m} = 200\text{ cm}\) and \(R = 1\text{ cm}\): \[h = \sqrt{2 \times 200\text{ cm} \times 1\text{ cm}} = \sqrt{400} = 20\text{ cm}\]
Thus, the depth of impounding near the bund is 20 cm.
समोच्च बांध के पीछे जलभराव की गहराई की गणना:
समोच्च बांध के पीछे जल एक त्रिभुजाकार वेज के रूप में एकत्र होता है:
\[h = \sqrt{2 \times \text{VI} \times R}\]
जहाँ
\(\text{VI} = 2\text{ m} = 200\text{ cm}\), तथा \(R = 1\text{ cm}\) \[h = \sqrt{2 \times 200 \times 1} = \sqrt{400} = 20\text{ सेमी}\]
अतः बांध के पास जल की गहराई 20 cm होगी।