Explanation :-

(i) Optimum number of rain gauges is calculated using the Coefficient of variation method, not the Double Mass Curve technique.

Required number of rain gauges,

N = (Cv/E)²

Where,

Cv = Coefficient of variation of rainfall data

E = Allowable error

Explanation :-

Super passage :

• A Super passage is a cross drainage work provided to carry a natural drain over a canal when bed of the natural drain is well above the canal F.S.L.
• It allows a natural drain to cross over an irrigation canal without interfering with the canal's flow.
• In Super passage bed level of the drain is much higher than the FSL (Full Supply Level) of the canal.
• A super passage is essentially the reverse of an aqueduct, where the canal is carried over the drain.

Solution :-

Return period (T) = 20 years

Probability of the rainfall occurring in a single year (p),

= 1/T

= 1/20

Probability of the rainfall occurring at least once in the next n (here, n =1 ) years (P),

= 1 - (1 - p)^n

= 1 - (1 - 1/20)¹

= 1 - 1 + 1/20

= 1/20

Explanation :-

Furrow Method of Irrigation,

• Furrow irrigation involves digging narrow channels (furrows) between crop rows, and water flows in these furrows.
• It is wetting only a portion of the land (1/2 - 1/5) surface, not the entire field.
• Furrow irrigation can be used on sloping land, but not suitable method for areas with very steep slopes, as it can lead to erosion and runoff.
• For steeper slopes, contour furrows or other irrigation methods like sprinkler irrigation might be more appropriate.

Solution :-

(1) For Rice crop :

Area, A = 1200 hectares

Base period, B = 140 days

Delta, Δ = 134 cms = 1.34 m

Duty of Rice (D),

= 8.64 × B/Δ

= 8.64 × 140/1.34

= 902.69 ha/cumec

Design Discharge of Canal (Q),

= Area/Duty

= 1200/902.69

= 1.33 cumec

(1) For wheat crop :

Base period, B = 120 days

Delta, Δ = 52 cms = 0.52 m

Duty of Wheat (D),

= 8.64 × B/Δ

= 8.64 × 120/0.52

= 1993.85 ha/cumec

For wheat crop Design Discharge of Canal (Q) will be same as rice crop.

Area irrigated for wheat crop (A),

= Design Discharge × Duty of wheat

= 1.33 × 1993.85

= 2651.82 hectares

Explanation :-

Lysimeter :

• It is a container filled with soil column and physically separated from the environment, with a known volume and cross-sectional area.
• It is used to measure water movement and evapotranspiration through the soil.
• It is used in various field like Hydrology and Soil Science, Environmental Monitoring and Agricultural Research.

Explanation :-

Manning's formula is an empirical equation used to estimate the velocity of flow in an open channel or pipe based on the channel's characteristics and the flow conditions.

Manning's formula,

V = (1/n) × R^(2/3) × S^(1/2)

Where,

V = Velocity of flow (m/s)

n = Manning’s roughness coefficient (dimensionless)

R = Hydraulic radius (m) = A/P

A = Cross-sectional area of flow (m²)

P = Wetted perimeter (m)

S = Bed slope

Solution :-

Optimum number of rain gauges,

N = (Cv/E)²

Where,

Cv = Coefficient of variation of rainfall data = 25%

E = Allowable/Admissible error = 5%

N = (25/5)²

N = 5²

N = 25

Solution :-

Mean Velocity (V) = 1 m/s

Silt factor (f) = 1

As per Lacey's theory, Hydraulic mean radius (R),

= (5/2)(V²/f)

= (2.5)(1²/1)

= 2.5 m

Explanation :-

Vadose water :

• It is also known as under-saturated water/capillary water.
• It is a sub-surface water located above the ground water table.
• The vadose zone (under-saturated/capillary zone) having pore spaces that are not fully saturated, but partially filled with water and partially filled with air.