Fluid Pressure & Fluid Velocity Confusion

[sanguinee]

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I seem to be a little confused with the correlation between fluid pressure and fluid velocity and was hoping someone could explain this to me.

In Bernoulli's equation, we see that the pressure increases whenever the fluid velocity decreases. However, why does blood pressure increase with sympathetic activation by decreasing the diameters of arterioles? With the equation A1v1=A2v2 and Bernoulli's equation, we would see a decrease in area, and increase in velocity, which should result in a decrease in pressure?

 

[aldol16]

Bernoulli's equation is talking about the entire system as a whole and compares two separate points in the system. For instance, one side of a bottleneck compared to another. You're talking about comparing the bottleneck at one time point to the same location at another time point. That's different. It's different because Bernoulli's equation is basically conservation of energy. You can talk about conservation of energy within a system but when what you're talking about isn't a system, it doesn't really apply. For example, I could say that when I open the refrigerator, some heat leaves the room and enters the refrigerator - an equal amount must leave that enters the refrigerator. That's conservation of energy. Now, what if I say a point 5 inches above the sink was at 273 K and now is at 270 K? Well, the temperature decreased. But I can't apply conservation of energy to compare 273 K and 270 K because these are inherently different conditions!