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I'm currently working on modeling a vacuum system in which a pump is present. the pump is driven at a varying speed $\omega$. The manufacturer has only given the characteristic curve at a single speed $\omega_{ref}$, which is well-approximated by a 3rd-order polynomial in the mass flow, that is:

$$\Delta p_{\omega=\omega_{ref}}(\dot{m}) = c_3\dot{m}^3 + c_2\dot{m}^2+c_1\dot{m}+c_0.$$

My model however requires this characteristic at arbitrary blower speeds. My current solution is to use the pump affinity laws, i.e.

$$\Delta p(\dot{m}, \omega) = \left(\frac{\omega}{\omega_{ref}}\right)^2 \Delta p_{\omega=\omega_{ref}}(\dot{m}),$$

however this leaves the curve rather "squished", almost like a straight line. Does anyone know of a different way of scaling the characteristic for different speeds?

I also have access to an experimental setup. Here I can impose the pump speed $\omega$ and measure back the pressure difference $\Delta p$, though the mass flow cannot be measured.

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  • $\begingroup$ for low vacuum stuff, you can infer mdot from the dp/dt rate of a big volume. remember to adjust for temperature. $\endgroup$
    – Pete W
    Sep 30, 2021 at 12:25

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