Static and Dynamic Pressure in a cyclindrical pipe

[ostritch]

I am making a basic structural engineering software program for modelling cylindrical pipes. I want to model the effect of fluid inside the pipes. For static fluid I let the user input the internal pressure and density of the fluid in each element. For moving fluid I additionally want to let them specify a velocity. This will let me calculate skin friction and centrifugal forces due to curved pipe sections.

The density and velocity are constant over pipeline. I know this is not very realistic due to losses and Bernoulli etc but it is satisfactory for my structural analysis purposes. I am now reading about dynamic pressure and how a moving fluid can exert an addition dynamic pressure given by

0.5 * ρ * V²

where ρ is the fluid density and V is the fluid velocity.

Is this pressure applicable in my case? If I add this dynamic pressure to the user-specified internal pressure, then this total pressure will be assumed to act in every direction. Each discreet element in my pipeline is open at the ends,as its joined to adjacent elements. Am I correct in thinking that the pressure can only act on the pipe walls? If the internal pressure is higher than the external pressure, the pipe will tend to bulge and including a poisson's effect, the element will tend to shorten. I'm not sure if it is correct to include the dynamic pressure with the user internal pressure in this calculation. My understanding is that the dynamic pressure acts only in the direction of the fluid velocity i.e. towards the end cap of the element. Since there isn't a physical end cap, does this mean that this dynamic pressure does not affect the element?

Thank you for your help, this has been bothering me for a while.

 

[MrMatt2532]

Take an element on the pipe wall. The forces felt on the wall due to the fluid are going to be the skin friction in the tangential direction and the pressure (aka the static/thermodynamic pressure) in the normal direction. Note that technically, in general, something called normal shear is another possible force, but it will almost certainly be negligible, especially in this situation. The pressure plus the normal shear is often called the "mechanical pressure". Again, this it mostly an aside.

Now, where does the dynamic pressure come in you ask? The dynamic pressure is just a term that means IF the flow stagnates (stops moving) isentropically (no losses/heat transfer), the pressure will rise by that amount. Let me explain with an example. In our atmosphere, the pressure is about 100000 Pa. Let's imagine you are moving at highway speeds in a car and holding your open palm out the window. Far in front of you the static pressure is 100000 Pa and the dynamic pressure is about 300 Pa and therefore the total or stagnation pressure is 100300 Pa. As the flow approaches your hand it will slow down and stagnate. Now, the static pressure is 100300 Pa, the dynamic is 0 Pa, and the total is 100300. As you can see, the dynamic was just converted into static and the total was maintained. At the end of the day, the normal force that is felt is still due to the static pressure.

Now, let's go back to your pipe question. For a straight, constant area pipe with gravity neglected, it can be shown that there is only changes in pressure in the axial direction. This means that the pressure in the center of the pipe is equal to the pressure on the walls of the pipe. There is not an increase in the static pressure because the flow is not going through this stagnation process anywhere. It is worth noting that there is an increase in the dynamic and total pressures at the pipe center relative to the walls of the pipe due to higher velocity, however again, the static pressure is constant because the flow isn't going through a stagnation process.

 

[ostritch]

Thank you very much for your detailed answer, it was very useful!