I am an engineering student designing a pipe system for a fluid flow and I calculated everything including the pressure loss. Now I have to choose a pipe material and pipe thickness for the piping system and I realized that I don't know the exact pressure in the pipe. I tried to calculate the pressure from the 'Bernollie Equation' but I cannot calculate it there either because I don't have a reference pressure point.

To explain it better, let's say I have a closed square system in the horizontal plane. The system contains 4 elbows 4 straight pipes and a pump that makes the circulation. If I know everything about the flow ( flow rates, density, viscosity, etc.) how can I calculate the maximum pressure in the pipe will encounter?

Sorry for my bad English, If there is a part that is not clear I can try to explain it again.

  • 1
    $\begingroup$ Does one end of your pipe open to atmosphere? If not, can you trace the path to the other side of the pipe wall (aka atmosphere) somehow? $\endgroup$
    – Abel
    Nov 16, 2023 at 13:21
  • $\begingroup$ Not a full answer, but if it's really a closed system, you'll need (in addition to the pressure differences from Bernoulli's law or (more likely) the Colebrook-White equation), knowledge of the bulk modulus of the fluid, the total mass of fluid present, the elastic properties of the pipe material, and the formulae for axial and hoop stress in an inflated cylinder. It will be a seriously hard calculation, and you may do better to redesign the system to have an opening to atmosphere somewhere. $\endgroup$ Dec 26, 2023 at 15:47

3 Answers 3


The pressure needs to be known at some point in the system if you want to calculate pressure distribution in the whole system. Flowrate is basically proportional just to the pressure difference, so the information about value of pressure at a point is not there. (Although if you know flowrate, viscosity, temperature and fluid, you might be able to infer the pressure from fluid viscosity dependence on temperature and pressure.)

For a pressure piping thickness design, you would need the difference between internal and external pressure. When this difference is positive, the calculation is simpler, because in the opposite case, unstable deformation (buckling) may by the expected failure mode and it is harder to predict.


First I’ll assume that the liquid has a negligible vapor pressure (it’s not a refrigerant for example.)
When you first fill the pipe with fluid it will be at atmospheric pressure as there is no elevation. As soon as the pump kicks in the pressure on the outflow of the pipe will increase and at the inflow drop. The max pressure in the system will be at the pump output.
You are probably using a centrifugal pump for fluids. The specs on the pump should give you the maximum head and this is what you should use as a minimum for the pipe pressure (plus a suitable safety factor). If the pipe becomes blocked anywhere (or someone closes a valve that they shouldn’t) this will be the maximum pressure in the system.


To calculate the maximum pressure in a pipe, you can use Barlow's formula. This formula can be used to determine the internal pressure at minimum yield, ultimate bursting pressure, maximum allowable operating pressure, and mill hydrostatic test pressure.

The formula is:

$$Pa = \frac{2 \cdot Sy \cdot Fd \cdot Fe \cdot Ft \cdot t}{do}$$


  • Pa is the maximum allowable design pressure (psig),
  • Sy is the yield strength (psi),
  • Fd is the design factor,
  • Fe is the longitudinal joint factor,
  • Ft is the temperature derating factor,
  • t is the wall thickness (in, mm),
  • do is the outside diameter (in, mm).

Please note that this formula is based on ideal conditions and room temperatures. You might need to adjust the parameters based on your specific conditions.

However, it's important to note that the pressure in a fluid system can vary depending on many factors, including the pump's operation, the fluid's properties, and the system's configuration. Therefore, it's recommended to consult with a professional or your professor to ensure the safety and efficiency of your design.

I hope this helps! If you have any other questions, feel free to ask. 😊

  • $\begingroup$ Equations that mix units from different systems, such as SI & US customary units are appalling. Is there a version of the equation that uses just SI units? $\endgroup$
    – Fred
    Nov 26, 2023 at 9:30
  • $\begingroup$ In any case, I think OP wants to know the actual pressure, not the maximum allowable pressure. $\endgroup$ Dec 26, 2023 at 14:25

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