Example Flow Through an Orifice

The next problem is flow through an orifice. If the pipe or channel is very small, the flow may be laminar. This is usually the case in microfluidic devices. If the channel is small, the 

Step 1 It is convenient to solve this problem in nondimensional form, because you want solutions for Reynolds numbers from 1 to 1000. For the lower Reynolds numbers, you use the equations in the form 

Step 3 For the higher Reynolds numbers, use the equations in the form 

The reason you need to do this is that the first method converges well for low Reynolds numbers, but not for high Reynolds numbers, and the reverse holds for the second method. 

Step 4 The inlet velocity is taken as a parabola with an average velocity of 1.0  

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