Final answer:
The sympathetic nervous system is responsible for providing the nerve supply to the kidney for the regulation of renal blood flow by modulating the dilation and constriction of renal arterioles, especially during stressful conditions.
Step-by-step explanation:
The nervous system division that provides the nerve supply to the kidney and regulates renal blood flow through dilation and constriction of the renal arterioles is the sympathetic nervous system. This system is activated in stressful situations and prepares the body for a "fight or flight" response. In contrast, the parasympathetic nervous system is active during restful periods and has no significant input to the systemic blood vessels, leaving the sympathetic system to determine their tone.
Within the autonomic nervous system, the sympathetic division innervates the kidneys via the celiac plexus and splanchnic nerves. During rest, reduced sympathetic stimulation leads to vasodilation and increased blood flow to the kidneys. In stressful conditions, however, sympathetic activity increases, causing vasoconstriction of the afferent arterioles, which leads to reduced kidney blood flow and thus decreased glomerular filtration. This response conserves blood flow for more critical organs in times of stress.