**Core Concept**
Free water clearance (C_H2O) is a measure of the volume of plasma that is cleared of solute-free water per unit time. It is an essential parameter in evaluating renal function, particularly in patients with fluid and electrolyte imbalances.

**Why the Correct Answer is Right**
The correct formula for calculating free water clearance is C_H2O = V x (U_osm / P_osm), where V is the urine flow rate, U_osm is the urine osmolality, and P_osm is the plasma osmolality. This formula takes into account the amount of solute-free water reabsorbed or excreted by the kidneys. The kidneys regulate the amount of free water by adjusting the amount of water reabsorbed in the collecting duct, which is influenced by the presence of antidiuretic hormone (ADH) and the osmolality of the blood.

**Why Each Wrong Option is Incorrect**
**Option A:** This formula is not correct because it does not account for the osmolality of the urine and plasma. Without considering osmolality, this formula would not accurately reflect the amount of free water reabsorbed or excreted by the kidneys.
**Option B:** This formula is incorrect because it includes the term "U_Cr", which represents the concentration of creatinine in the urine. Creatinine clearance is a measure of glomerular filtration rate (GFR), not free water clearance.
**Option C:** This formula is not correct because it includes the term "P_V", which represents the plasma volume. Free water clearance is a measure of the volume of plasma cleared of solute-free water, not the total plasma volume.

**Clinical Pearl / High-Yield Fact**
In patients with diabetes insipidus, free water clearance is often elevated due to the inability of the kidneys to reabsorb sufficient amounts of water, leading to excessive urine production and polyuria.

**Correct Answer:** C. V x (U_osm / P_osm)