Effect of changes in pressure on flow

[thushan]

Suppose we had a rigid tube full of fluid with a pressure head.

Now suppose we changed that pressure instantaneously. Would the flow instantaneously increase to its new value (as per (P = FR), or would the flow increase over time until it reaches the new value?

My gut feeling is the latter, since pressure is effectively a force on a particular unit of area, and force is a product of acceleration. My guess would be that the fluid will accelerate with the increased pressure head, until the resistance of the vessel increases its friction force (which is a function of the velocity of the fluid?) to equal that of the pressure head.

Would circumstances be different if the tube were relatively compliant?

Btw - this is for cardio physiology, but it's a physics concept and I don't have the sufficient background.