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I have a centrifugal pump (Q: 64 m3/hr, H: 30 m) connected to a balance tank but it can't provide enough flow for my purpose. One quick option is to add a firefighting truck's piston pump to the circuit. I'm not sure about the features of the pump but I'm sure it delivers more flow and pressure than the centrifugal pump. My question is, do I have to worry about back flow when I'm not using none-return valves?

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If you pump into the same pipe, then yes, you will need to worry about these. You'd need check valves or such, and the performance of the pair would be lower than just sum of the two performances.

But the easy solution is to draw two separate pipes to the balance tank - make the tank be the point where the two flows meet. That way one flow won't interfere with the other, until the tank overflows.

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Yes, you would - the more powerful pump will discharge or stall it through the other wasting energy and time.

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