EK FL 3 C/P #8

ThujaOccidentalis

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The answer says pressure decreases with a more narrow pipe. I thought the more narrow the pipe = more often molecules will collide with the pipe, thus increases pressure.

And what about vasoconstriction? When you constrict blood vessels, you decrease the radius (more narrow) but blood pressure increases. How does that work and what's the difference between the two scenarios?

TheLongGame

2+ Year Member
FLUIDS!!!!

Okay, so we need to start with understanding that the energy and mass of the fluid is going to be conserved. So taking Bernoulli's equation, assuming a horizontal pipe here, we can set the total energy of the "Fat" pipe equal to that of the "Skinny" pipe:

P1+1/2(rho)(velocity1)^2 = P2+1/2(rho)(velocity2)^2

P1 = pressure of fat pipe
v1 = fluid velocity of fat pipe

P2 = pressure of skinny pipe
v2 = fluid velocity of skinny pipe

So, understanding that the volumetric flow rate is going to remain constant, we know that in the skinnier pipe, the fluid velocity must be faster. In order to balance the equation, the pressure must change in the opposite direction of the velocity. So if velocity increases, the pressure must decrease. Simple algebra will lead you to this conclusion...Now on to your second question...

The reason why pressure increases in vasoconstriction is because the volumetric flow rate is different "at rest" than it is during vasoconstriction. We know this because the body is shunting blood away from non-vital systems in order to achieve some desired state. That is KEY difference between the two scenarios Let me know if you still have any questions!!!!