You're absolutely right! Blood vessels are constricted, but in the visceral organs (i.e. gut organs) and skin, while the skeletal muscle blood vessels are dilated. This occurs because it induces the shunting of oxygenated blood toward the skeletal muscles which helps facilitate the flight-or-flight response by efficiently facilitating abundant ATP in important muscles.
Now, vasoconstriction is simply caused by the contraction of smooth muscle cells on the inner lining of the arterioles, Poiseuille's Law indicates the vessel pressure is inversely proportional to the radius of the vessel to the forth power, indicating that a very
tiny change in smooth muscle conformation is responsible for
BIG changes in pressure (Poiseuille's Law:
http://hyperphysics.phy-astr.gsu.edu/hbase/ppois.html ; its not necessary to memorize, but its good to look at the math to better understand the concept). Smooth muscle contraction and relaxation is a very efficient way for the body to control blood pressure in the short term.
The mechanism that induces vasoconstriction is a tad more complicated though. As you've mentioned, the sympathetic nervous system uses epinephrine and norepinephrine as their post-ganglionic neurotransmitters to induce desired effects on target organs. Long story short, there is a group of receptors called beta-adrenergic receptor (any adrenergic receptor is one that binds to epinephrine/norepinephrine, aka, adrenaline/noradrenaline). Binding of beta-adrenergic receptors (at a variety of sites including vessels, heart, and kidneys) with the respective neurotransmitter induces a flurry of cellular responses, one of which is vascular smooth muscle contraction in arterioles. Binding of beta-adrenergic receptors in the kidneys induces the release of Renin, and enzyme responsible for the proper activation of angotensin II, which further increases blood pressure through inducing the secretion of aldosterone from the adrenal cortex, among other effects.
I think that summarizes it fairly well. Let me know if you have any questions!
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