Estimating circular pipe flow velocity through a known elevation profile and known length with a known initial pressure and flow velocity

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?

• surely the mass flow rate is constant? or do you have leaks? Sep 11 at 15:16
• @SolarMike is right, a pipe has to have the same velocity all the way through it unless the density of the fluid is changing. Sep 11 at 17:52
• Liquid water is approximately a incompressible fluid, meaning its volume changes very little regardless of what pressure is placed on it. It is however susceptible to temperature and phase change (if you are sucking water it might apply; call it steam if it gasifies). Regardless, info you do not mention is required- if incompressible, flow velocity in m/s is a function of your known velocity and pipe area. If compressible you need to figure out density changes which will be driven by a variety of factors like temperature and pressure.
– Abel
Sep 11 at 18:12
• The flow velocity could be accelerated due to gravity and if the fluid does not always cover whole pipe cross section, the velocity actually might be variable along the length. It would basically be (partially) open channel flow. Sep 12 at 20:20