Calculation of Volume of Water Retained in Aquifer

Given:
- Porosity of unconfined aquifer = 28%
- Permeability of unconfined aquifer = 30m/d
- Specific yield of unconfined aquifer = 0.22
- Area of unconfined aquifer = 50 km^2
- Fall in water table = 0.10 m

Steps to Calculate the Volume of Water Retained in Aquifer:

1. Calculation of Storage Coefficient:
The storage coefficient (S) is the product of the porosity and specific yield of the unconfined aquifer.
S = Porosity x Specific Yield
S = 0.28 x 0.22
S = 0.0616

2. Calculation of Change in Water Storage:
The change in water storage (ΔS) is the product of the storage coefficient, area of the aquifer, and the fall in water table.
ΔS = S x Area x Change in Water Table
ΔS = 0.0616 x 50 km^2 x 0.10 m
ΔS = 0.308 km^3

3. Conversion of Volume to Other Units:
The volume of water retained in the aquifer can be expressed in different units like liters, gallons, or acre-feet.

- 1 km^3 = 1,000,000,000,000 liters (approximately)
Therefore, the volume of water retained in the aquifer is approximately 308,000,000,000 liters.

- 1 km^3 = 264,172,052,358.15 US gallons (approximately)
Therefore, the volume of water retained in the aquifer is approximately 81,419,680,000 US gallons.

- 1 km^3 = 810,713.1782 acre-feet (approximately)
Therefore, the volume of water retained in the aquifer is approximately 249,648.6 acre-feet.

Conclusion:
The volume of water retained in the unconfined aquifer with an area of 50 km^2, porosity of 28%, permeability of 30m/d, and specific yield of 0.22 when the water table falls by 0.10 m is approximately 0.308 km^3 or 308,000,000,000 liters or 81,419,680,000 US gallons or 249,648.6 acre-feet.