Yes, you�re absolutely right to think that the volume of urine produced following immersion in cold water is greater than that produced when the body is immersed in water at near body temperature.
The first thing that happens following immersion in cold water is that vasoconstriction occurs. This in turn, causes blood to be directed away from the skin surface of the body to deeper blood vessels, mainly veins. Veins can carry this increased volume of blood because they have the ability to stretch to relatively huge diameters.
Now, when all the blood vessels in the body carry the optimum quantity of blood, the heart maintains a fairly steady input-output rate. However, when the blood circulates in mainly core blood vessels, as it does during vasoconstriction, there is an increase in the venous blood return to the heart.
This increased venous blood return causes the atria in the chambers of the heart to enlarge or distend. These atria contain special cells that release a hormone called Atrial Natruretic Factor (ANF) that increases diuresis. Also, nerve receptors in the atria send a signal to the brain to decrease the production of ADH, resulting in further increased urine production.
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