Question

What is the relationship between porosity and specific yield?

• A. Porosity is greater than specific yield
• B. Specific yield is greater than porosity
• C. Porosity and specific yield are equal
• D. Porosity and specific yield are independent of each other

Hint:

• Porosity ($n$) is the total pore space.
• Specific Yield (S$_y$) is the part of pore water that drains by gravity.
• Specific Retention (S$_r$) is the part of pore water retained against gravity.
• $n = S_y + S_r$.
• Since $S_r \ge 0$ (and usually $S_r>0$ for water-bearing materials), then $S_y \le n$.
• This means porosity is generally greater than specific yield.

Answer 1

The Correct Option is A

The relationship between porosity, specific yield, and specific retention is fundamental in groundwater hydrology:

• Porosity ($n$): The total volume of void or pore space in a rock or soil, expressed as a fraction or percentage of the total volume. It represents the maximum amount of water the material can hold when saturated.
• Specific Yield (S$_y$): The ratio of the volume of water that a saturated rock or soil will drain by gravity to the total volume of the rock or soil. This is the water that can be practically extracted from an unconfined aquifer.
• Specific Retention (S$_r$): The ratio of the volume of water that a saturated rock or soil will retain against the pull of gravity (due to molecular attraction and capillary forces) to the total volume of the rock or soil. This water remains in the pores even after gravity drainage.

The key relationship is: Porosity ($n$) = Specific Yield (S$_y$) + Specific Retention (S$_r$) Since specific retention (S$_r$) is always a non-negative value (S$_r \ge 0$), and in most materials S$_r>0$ (some water is always retained), it follows that: Specific Yield (S$_y$) = Porosity ($n$) - Specific Retention (S$_r$) This means that specific yield (S$_y$) is always less than or equal to porosity ($n$). S$_y \le n$ Or, rephrasing, Porosity ($n$) is greater than or equal to specific yield (S$_y$). In practical terms, S$_r$ is almost always greater than zero for natural earth materials, so S$_y$ will be strictly less than $n$. Therefore, porosity is greater than specific yield (unless S$_r=0$, which is highly unusual for natural materials that can hold water). Option (a) "Porosity is greater than specific yield" is the correct relationship, assuming S$_r>0$. Option (b) is incorrect. Option (c) would only be true if S$_r = 0$, which is not typical. Option (d) is incorrect as they are directly related. \[ \boxed{\text{Porosity is greater than specific yield}} \]