# Pressure changes in Continuity equations and Poiseuille's Law? Continuity says Q=AV, and we know t

Pressure changes in Continuity equations and Poiseuille's Law?
Continuity says Q=AV, and we know that velocity and pressure are inversely related. So if we are in a closed system, like vasculature for example, Q is constant and any decrease in vessel radius would be expected to raise velocity, which would result in lower pressure.
If we look at Poiseuille's Law, on the other hand, we see the opposite! If Q is constant, then a decrease in radius/cross sectional area we should expect pressure to be raised!
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Ellie Meyers
Bernoulli is a statement of the law of conservation of energy for an ideal (non vicious) fluid. Poiseuille relates to situations where fluid friction is present so you cannot expect the results to be the same.
If you use Bernouilli for an ideal fluid through a horizontal tube of constant cross sectional area, no pressure difference is needed across the tube to move the fluid through it, ie the fluid moves through the tube with a constant kinetic energy and no work needs to be done.
The situation changes if there is fluid friction and work has to be done to keep the kinetic energy of the fluid constant.
That work is done as a result of the pressure difference across the tube.
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Yasmine Larson
Pressure always increases when velocity decreases (and vice-versa) only for an inviscid fluid. If the fluid is viscous, then this is not necessarily the case. For flow of an inviscid fluid through a pipe of constant cross section, the pressure is constant. For flow of a viscous fluid through a pipe of constant cross section, the pressure decreases in the flow direction. So, for a real viscous fluid, one of these two effects is going to win out. That depends on the specific geometry of the conduit, the mass flow rate, and the viscosity of the fluid.