What is the relationship between pressure and flow rate in a pipe?

[lluke9]

What IS Pressure-- in a pipe?

Whaddup, guys! Sorry to bug you with another question.

So, I learned that Pressure = Force / Area. Pretty easy stuff. Water will exert a certain amount of force per area depending on how deep the object is submerged.

But... what about in a pipe?
There's Bernoulli's Equation, P + .5ρv² + ρgh = P + .5ρv² + ρgh, which can be used to find pressure changes in a pipe with different flow rates (the typical hourglass-shaped pipe comes to mind).

So, question:
But what is this "pressure" in this pipe? If pressure is force over area, where does the water exert this force? Like, exactly where? Does it exert it outwards against the pipe walls, or does it exert it... upon itself? What?

That my instructor managed to skip over this thing bugs me a bit. Is it not important?

 

[Curl]

Exerts it everywhere, more or less with the same magnitude depending on the amount of turbulence. It pushes on the pipe wall as well as on the adjacent fluid which is what makes the flow dynamic.

 

[josftx]

Seeing your ecuation from a different point of view we had

$\frac{P_{1}}{\rho g} + \frac{v_{1}^{2}}{2g}+z_{1}=\frac{P_{2}}{\rho g}+\frac{v_2^{2}}{2g}+z_{2}$

The therms like $\frac{P}{\rho g}$ is related with the static pressure and this relationship with the pressure that the fluid exerts on the walls of the pipe. like when you have a hosepipe and you open the key and the hosepipe blow up.

The therms like $\frac{v^2}{2g}$ calls the dynamic pressure and its related with the movement of the infinite elements of fluids that make up the flow and impulse the fluid outside the hosepipe. The above ecuation neglect the losses of friction and when you want to use the formula $P=\frac{F}{A}$ you can use the static pressure in the walls for determinate with some relations of solids mechanics, for example the minimun thickness of the walls of the pipe or some like that.