Calculation of Change in Storage

Given:
Area (A) = 50 hectares
Change in water table (Δh) = 3 metre
Porosity (n) = 0.30
Specific retention (S_r) = 0.10

The change in storage can be calculated using the following formula:

ΔS = A × Δh × n × (1 + S_r)

Substituting the given values in the formula, we get:

ΔS = 50 × 3 × 0.30 × (1 + 0.10) = 45 hectare metre

Therefore, the change in storage in hectare metre is 45, which is option C.

Explanation

The given problem is related to the calculation of change in storage in an irrigable area when the water table drops by a certain depth. The concept of porosity and specific retention is also involved in this problem. Let us understand each concept in brief.

Porosity: It is the ratio of the volume of voids to the total volume of the soil or rock. In other words, porosity is the measure of the amount of empty space or voids in the soil or rock. It is expressed as a percentage or decimal.

Specific retention: It is the amount of water that a soil or rock can retain against the pull of gravity. It is expressed as a percentage or decimal.

Now, let us see how these concepts are used to calculate the change in storage in the given problem.

Calculation of Change in Storage

The change in storage can be defined as the difference in the amount of water stored in the soil or rock before and after a change in the water table. It can be calculated using the following formula:

ΔS = A × Δh × n × (1 + S_r)

where
ΔS = Change in storage in hectare metre
A = Area in hectares
Δh = Change in water table in metre
n = Porosity
S_r = Specific retention

Substituting the given values in the formula, we get:

ΔS = 50 × 3 × 0.30 × (1 + 0.10)
ΔS = 45 hectare metre

Therefore, the change in storage in hectare metre is 45, which is option C.

Conclusion

In conclusion, the calculation of change in storage is an important aspect of water resources engineering. It helps in determining the amount of water available for irrigation, domestic use, and other purposes. The concept of porosity and specific retention plays a crucial role in this calculation.