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For example, I have a pipeline which is 2" and 6.5 km long. I worked the volume out using πr² × height so π×0.0254m²×6500m which is 13.17m³.

How do I now determine how much more water I require to increase the pressure to 10 barg?

I know the material of the pipeline matters but I am just looking for a ballpark not exact accuracy. I also know that temperature matters but for this case lets say the temperature remains constant again this is because I require a ballpark figure.

It is for a hydro test (pressure test) of the pipe. we are taking it up to 150% of its design pressure which is 414 barg so 621barg