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Orifice flow, temperature/viscous effects

Orifice flow, temperature/viscous effects

Orifice flow, temperature/viscous effects

I have a general question on flow through an orifice for varying temperatures/viscosities. For a given pressure drop and orifice size, intuitively I would expect a colder, more viscous oil to have less flow through the orifice than oil at temp. However from looking at the Reader-Harris/Gallagher equation for discharge coefficient, the coefficient of discharge is inversely related to the Reynolds number. Since Reynolds number is inversely related to to fluid viscosity, this would suggest to me that a more viscous fluid will have a higher discharge coefficient, resulting in more flow through an orifice for a given pressure drop relative to the less viscous fluid at temp. Which does not seem intuitive to me. Is this correct or can someone help point me to what I'm missing here? Thanks in advance.

RE: Orifice flow, temperature/viscous effects

If that can help you:
For hydraulic oil of density 0.932 in a thin-walled nozzle the flow rate is = 0.5 ø² (dP) ^ 0.5. For a low pressure or a high viscosity I multiply the flow rate by a coefficient V.
If necessary I have the formula of the coefficient V for calculation on a computer

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