Calculate Flow Rate From Pressure at Two Points?

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To calculate flow rate from pressure at two points, the Darcy-Weisbach equation is recommended for determining flow through a pipe, particularly for irreversible pressure drops. Flow rates can vary significantly, ranging from 100 sccm to 500 sccm. Understanding the relationship between pressure and flow rate is crucial for accurate calculations. Additional resources and equations may also be useful for specific scenarios. Accurate flow rate determination is essential for various applications in fluid dynamics.
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I am trying to find out what is the best method / correct formula to calculate Flow rate at inlet/outlet when pressure is known. Please see attached image. any help would be greatly appreciated.

Note: Flow Rate can Vary from 100 sccm to 500 sccm.

Flow Calc.png
 
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For simple comparison, I think the same thought process can be followed as a block slides down a hill, - for block down hill, simple starting PE of mgh to final max KE 0.5mv^2 - comparing PE1 to max KE2 would result in finding the work friction did through the process. efficiency is just 100*KE2/PE1. If a mousetrap car travels along a flat surface, a starting PE of 0.5 k th^2 can be measured and maximum velocity of the car can also be measured. If energy efficiency is defined by...

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