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calculate backflow (leak rate) through closed reed valve

calculate backflow (leak rate) through closed reed valve

calculate backflow (leak rate) through closed reed valve

(OP)
I'm looking to calculate the steady backflow (leak rate) through a closed reed valve, given the pressure difference and the viscosity of the fluid.

For simplicity, the reed is circular with radius R, and is sitting over a hole with radius r. The reed remains flat and so contacts the flange over an (R-r) anulus.

I'm not even sure what is the principal mechanism by which backflow occurs...
- Is the flow due to surface imperfections?
- Is there a thin film of fluid that is held together by surface tension?
- Is there a mechanism by which equilibrium is reached? specifically: if the reed is in equilibrium, then the pressure on both sides of the reed (over the contact area) equalizes. removing most of the seating force

Thanks,
  Ben.

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