Aquifer storage terms in groundwater hydrology:\r If n is porosity, y is specific yield, and r is specific retention of a soil or rock, which relationship is correct?

Introduction / Context:
Porosity and its partitions govern how much water an aquifer can store and release. Specific yield and specific retention split porosity into a drainable portion and a portion held by molecular and capillary forces. Recognizing their algebraic relationship is essential for well design and groundwater balance calculations.

Given Data / Assumptions:

• n is total porosity (void volume / total volume).
• y (specific yield) is the fraction of water that drains by gravity.
• r (specific retention) is the fraction retained against gravity.

Concept / Approach:
By definition, total pore water divides into two mutually exclusive parts under gravity drainage: drainable (specific yield) and retained (specific retention). Therefore, their sum equals total porosity. This identity underlies volumetric water budget computations in unconfined aquifers.

Step-by-Step Solution:
Start with total porosity n.Partition into y (drainable) and r (retained).Thus: y + r = n.

Verification / Alternative check:
Laboratory drainage curves and field specific yield measurements confirm that the difference between porosity and specific retention equals specific yield for typical granular soils.

Why Other Options Are Wrong:

• Adding n to either side (e.g., n + y + r = 1) mixes dimensional fractions incorrectly.
• Equations setting n + y = r or n + r = y contradict the basic partition concept.
• n + r + y = 0 is non-physical since all are positive fractions.

Common Pitfalls:

• Assuming y equals n; fine-grained soils have large r, so y can be much smaller than n.
• Using porosity instead of specific yield in groundwater storage-change calculations, leading to large overestimates.

Final Answer:
y + r = n