A faced vapour pressure can not be eliminated even by increasing the vessel dimensions

First, look at the steady model run before the transient run. It look as if the normal static pressures in your system may be very close to zero such that any transient at all will drive it negative. Check the ground elevations you are using and the water level in the storage tank. I would have expected the hydraulic grade line to be on the order of 40 m above the ground but if the tank water level is at ground level, then you don't have much pressure.

the pipeline is just a transmission line and no need to high residual pressure, moreover in case of removing the air valve the model indicates a positive values and a small vessel is sufficent

Hello Mohammed,

What Tom is saying is that if your initial pressure is low, there is a higher chance of negative or vapor pressure conditions during a transient.

In general, an air valve will only protect against negative pressures in the immediate vicinity of the air valve and if the outflow orifice(s) are not sized properly, they can cause worse transients than the ones they were meant to protect against. See more background information here: Modeling Reference - Air Valves

In your model, air enters the air valve after the pump shutdown at 5 seconds, but that air pocket is subsequently expelled at ~6.8 seconds. An upsurge occurs as a result of the air pocket collapse, which then reflects back as a negative pressure wave. If I morph the air valve into a junction, pressure is still negative at the knee of the pipeline. A smaller size air outflow orifice can help cushion the air release to reduce this upsurge. See more here: Transient pressure worse with air valve added

Regarding the hydropneumatic tank - you may need to try placing it closer to the pump (between the pump and the air valve). It will not be able to protect the high point against the impact of the downsurge wave because it is downstream of that high point / knee.

I also noticed that there is an intermediate junction directly upstream of the air valve, at the same elevation. The downsurge wave front will reach this node before it reaches the air valve.

I strongly recommend animating the profile path in the Transient Results Viewer.

Dear Jessie

thank you for your useful reply i tried to throttle a valve at the downstream and increase the head of the pump, the protection worked

Dear Jessie

thank you for your useful reply i tried to throttle a valve at the downstream and increase the head of the pump, the protection worked