# Brains, Kinked Veins, and Pressure [closed]

My physics has degraded from mathematical to intuitive, always a problem. Asking for help with what appears to be a simple problem that starts here:

fluid flowing in a tube at a given flow rate encounters a constriction reducing the area of the tube. This will create a pressure gradient related to Bernoulli's Principle;

I need clarification on the relationship between that pressure gradient under conditions of increased flow (volume/time)? Is this linear or exponential?

• Might this help? As a first approximation you can model a constriction as a succession of contraction and expansion in the pipe. – Deep Apr 4 '18 at 14:12

If the speed goes up, the pressure goes down by the square because $\rm{P}+1/2\rho V^2$ doesn’t change.