Is there a simple equivalent to Ohm's law for gas (pressure$=R*$throughput)? Question
I have the feeling gas cannot have an equivalent of Ohm's law, tying pressure and throughput via some kind of fluid resistance constant depending on the geometry of the obstacle considered. Certainly because gas can be compressible.
However I need a very rough estimate (not a number from experience, a first order model/formula) of the air throughput out of an obstacle of arbitrary geometry of which I know the hollow cross sectional area. 
I have done my research but all I can find is Poiseuille's law or pipe flow formulas which apply to very long cylinders (what about if I'm looking at the "resistance" of a complex obstacle?)... And the venturi equation:
$$p_i-p_o=1/2(\rho_o v_o²-\rho_i v_i²)$$
With (conservation of mass flow)
$$\dot{m}=\rho_i A_i v_i=\rho_o A_o v_o$$
Which gives
$$\dot{m}=\sqrt{\frac{2(p_i-p_o)}{\frac{1}{\rho_o A_o^2}-\frac{1}{\rho_i A_i^2}}}$$
Knowing that
$$\rho=\frac{m}{V}=\frac{\frac{PVM}{RT}}{V}=\frac{PM}{RT}$$
(M is the molar mass of the gas, R the perfect gas constant)
Is it correct? It's not linear like Ohm's law, but it is a relationship.
Application
I would like this question to be generic, but as an application/illustration, attached is a simplified 3D model of the orifice - the scale is 15mm. I know the area of the side triangles and the front rectangle out of the conduit (top), and I'm wondering what the mass flow is through it. 

 A: An equivalent Ohms law can be applied to gas flow and pressure drop, but only for particular mechanical flow restrictions and limited to a range of flow. But more generally for orifices and tubes the relationship between pressure and flow is quadratic,  explained predominantly by the energy equation for flow, also known as Bernoulli's equation.
In the testing of respiratory equipment, companies like Hans Rudolph provide 'linear' flow resistors which approach the ideal linear resistor given by Ohms law. The restrictions in these resistors are accomplished with a screen like diffuser, and their linearity is specified over a restricted range.
So geometry does govern the relationship,  but to determine what geometry is required takes CFD software or repeated experimentation.
A: Application that you have considered is pipe flow. Pipe flow can be assumes as isentropic flow. Isentropic equations are non-linear. (Non-linear i'm using here is algebraic non-linearity. Please note the governing equation of fluid mechanics is  also non-linear PDE). So resulting gas equation will be non-linear in nature.
We know ideal gas relation is 
$p=\rho R_{specific} T$ . This Ideal gas equation can be linearized or make similar to Ohms law if we consider either constant temperature process or constant density process else this is always non linear. I'm sorry to say that, I'm not aware of any easy experiments to visualize that, melting and evaporation are isothermal process. Its tough to do qualitative analysis in those process without equipment. 
"Nature is non-linear. Linearity is a sub case of non-linearity".
A: This it not a propper answer, but something to think about. Let's talk DC first, if one applies a DC voltage, to a speaker, other than heating it up, its voice coil would move either backwards or frontwards, according to polarity, right? What if I hermetically seal two earphones to syringe like tube, at each end, with a piston that somehow has a 0 position (this 0 position may be obatained with springs, or, magnetically if it's a metallic piston, you name it) and apply DC to one of the phones? I think, if it pulls the voice coil on one side, which will pull the piston, it will pull the voice coil on the other side and vice versa, which I guess, intuitively, it would produce reversed polarity voltage on the passive earphone's terminals. Also, if an external force is applied to the piston, against the force inducted onto the piston, it would attenuate or even null the current trhough the voice coil to which the voltage was applied. If my assumption is correct, I suppose the same would happen with AC voltages. I guess such hypothesis, if right, would be an anology of ohm's law.
