I see a number of flaws in your argument.
Bucket model for the explain stenosis you suggest to use is not the "one tube is very large and one tube is tiny", it is "tubes are the same size, but one tube is narrowed (tiny) somewhere in the tube
This argument makes absolultely no sense. The scenario you suggest of a large tube that is narrowed is the exact same as mine. What counts is the cross sectional area of empty space through whic fluid could pass or inner diameter. If your argument was correct, I could get more flow through a tube if I increase the thickness of its walls. Think of your pumbing. Would increasing the thickness of the pipes while leaving the inner diameter change anything?? Undoubtedly not.
The following argument also does not make any sense.
Because the exit flow speed from tubes (v) is v=sqrt(2*9.81*dh);
where dh="diference in high between tube exit and bucket water level".
If both tube ends are on the same level and the buckets are also, then dh1=dh2 and then v1=v2.
Both tubes have the same cross section (A) at the exit end (A1=A2).
The rate of flow (or voume of flow per second, Q) at the end of both tubes is Q=A*v and is the same for both the tubes (Q1=Q2). It doesn't change during the whole tube - it is constant.
Only what is changing is velocity in the narrowed tube, but only at the location of narrowing (velocity increased to drive the same flow thru smaller crosssection).
From your argument, velocity of flow in a vertical tube is a function of just gravity (9. and DH. The diameter of the tube should therefore not affect velocity. In the scenario of the two buckets, velocity through the larger and smaller tubes would be the same.
You also mention that both tubes have the same cross sectional area, as you are using outer diameter. This is not correct as you need to use inner diameter. If you use inner diamter your formula will state that flow is reduced in the smaller tube.
I will make one last attempt to convince you that flow is reduced in the face of a stenosis. Here is another model:
Imaginge a closed loop system with a heart pumping blood at a certain cardiac output of lets of litres per minute. This closed loop system consists of a tube coming out or the heart and then going back into it. Let us assume that this cardiac output stays constant even in the face of a stenosis. In this scenario, as you would predict, there would be no reduced flow if you compare the system of the stenosis vs the system with no stenosis. What differs however is that velocity is higher through the stenotic portion. Another difference is that pressure would be higher before the stenosis and lower afterward.
Now take this system and modify it a bit. After the tube comes out of the heart, have it split into two tubes. Then have the tubes join together to form one tube which then goes back into the heart. What happens if you create a stenosis in one of these tubes? What will happen is that more blood will go down the tube without stenosis and less blood through the stenotic tube. As stenosis increases, less and less blood will get through this tube. When stenosis reaches 100% no more blood will go through the blocked tube and all of it will go through the patent tube. This scenario is closer to what happens in reality. It is common sense, intuitive and make sense from a mechanics point of view.