I've learned fluid dynamics but does not have much knowledge about its real-world applications.
My question is about the static pressure of a closed-loop pipe.
[Fig. 1. Pipe network. Source: Wikipedia Pipe_network_analysis]
According to the pipe network analysis, two conditions are satisfied for a steady-state closed-loop pipe flow.
- At any junction, the total flow into a junction equals the total flow out of that junction.
- Between any two junctions, the head loss is independent of the path taken. This is equivalent mathematically to the statement that on any closed loop in the network, the head loss around the loop must vanish.
I can understand above fundamental laws for the pipe network analysis.
However, I have difficulty analyzing the static pressure of each junction (not the head loss between two junctions).
Let a pump is located between J3 and J6 of Fig. 1.
Then following conditions will be hold:
- $Q_{in}=Q_{out}$
- $P_{6} - P_{3} =$ (actual head loss of the pump)
- $(P_{6} - P_{3})$ and $Q_{in}=Q_{out}$ are related by the pump characteristic curve.
Above five (2+3) conditions just tell about the pressure difference, not the absolute pressure value itself.
If the pump is turned off (i.e. no flow and no head loss) and there is no valve, each joint would have a same absolute pressure value which is determined by the total volume and mass of the fluid filled within the pipe network.
However, what will be the absolute value of $P_{3}$ and $P_{6}$ when the pump is operated?
Does the absolute pressure of each joint maitain a steady value for a steady pipe network?
If so, which factor determines the steady-absolute pressure value of each joint?
Or, can the steady-absolute pressure value vary depending on transient fluctuations during the pump turn-on period?
Or, can the absolute pressure value vary even for a steady pip network?