volumetric flow rateQ in a circular pipe is given by Poisseilli law which states that the flow rate is proportional to fourth power of radius of the tube. This is standard formula can be taken from any fluid mechanics books. If pressure drop and radius are given Q can be found.

Thank you sir. But in my case. its not a 1-D streamlined ,steady state flow. Actually here the pipeline that had a steady flow with say 60 kg/sq.cm. pressure at the pump station discharge is made to shut down, but the pipeline remains pressurized at say 55 kgs. Now, theives made a small hole(after fixing a leakproof clamp) in the underground pipe at an unknown distance say a few kilometers away. the flow (leak) now is through the clamp with much smaller diameter(unknown) in a direction perpendicular to the pipe axis. Now I am trying to relate the pressure fall noted at pump station to the quantity of leak/theft fluid(petroleum).

Ramana Sir: I am not sure, but I was thinking whether & how to use Bulk modulus concept for relating the pressure drop with the volume of fluid lost. Bcoz, when we start the pump & air is bled off, we observe that as the pipeline is completely filled the pressure gauge shows 'zero', but as the pump is allowed to run within seconds the pressure rises to higher values. thus, there is some amount of compression taking place in the fluid. But, on the other hand I have learnt that liquids are incompressible.... :(

The amount of leaked fluid is composed by two terms. First is the diferential of specific volume betwenn one and the other pressure, some times not very high value. The other volumen is the diffential of volume between a pipe under high presure and low pressure, due to the deformation of the pipe under pressure.

I think the easiest would be to perform pressure measurements at various points in the pipeline accurately time reading . With these measures through a study of transient would be possible to find out where the leak is.

thanks Carlos & Rogerio. Rogerio: we don't have the facility to measure Pressure at every point. But we may approximately get the pressure using Pascal's law as initially its a hydrostatic condition that changes to transient as the leak starts.

But one thing is there, that is, the pressure drop is transmitted both upstream & down stream (at the speed of sound in diesel) & is recorded at our pump stations. if we could relate the pressure values at the upstream & downstream stations, we should not only get approx. value of instantaneous pressure at the leak site, but also the location of leak site(by noting the time taken by pressure pulse to reach the upstream & downstream stations).

Carlos: please tell how could we determine the deformation of pipe. should we use the hoop stress concept for the same. is there any equation for transient analysis?

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Need not be measured in many ways, only with the ends is possible to evaluate the breaking point in an approximate way, but if there are two or more measurement points along the line would result mellhor.

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Warning, do not take the speed of sound, look in a book "fluid transients" (as the Streeter) an equation closer to reality.

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thank you Rogerio Sir.