I have a known elevation profile spanning the length of my pipe (~600 meters). An elevation value is given for every five meters of pipe. At the beginning of the pipe, I have a known velocity (1.1 m/s) and a known water pressure (0.1 bar) at the inlet of the pipe. The roughness and dimensions of the pipe are known. Is there any way to predict the velocity of water at each of the elevation data points through the length of the pipe?
Velocity is not necessarily constant thru-out pipe length. Density in terms of mass/pipe len can vary. Assume a baffle in the pipe.
The way I'd approach this problem is I'm thinking Bernoulli as soon as I see flow in a pipe. Have a look at Example 1 - https://study.com/skill/learn/how-to-use-bernoullis-equation-to-calculate-a-velocity-for-fluid-inside-a-pipe-explanation.html
As your resolution is 5 meters (h is specified for every 5 meters), I'd apply the formulas from Step 2 and 3 for every 5 meters. You can write a short script in your coding language of choice or ask ChatGPT to do it.
This method doesn't take into account the roughness of the pipe so far, which will influence how much pressure you're losing every X meters (5 in your case). Have a look at the pressure loss equation on Wikipedia: https://en.wikipedia.org/wiki/Darcy%E2%80%93Weisbach_equation
Again, you'd want to adjust for pressure losses every 5 meters. As your loss will compound for every iteration, you'd want to apply the pressure loss before calculating the next 5 meters etc...
The velocity from each point you can then put in a list and plot it. Piping engineers correct me if I'm wrong ...
