It is said that the less we open the throttle the slower is the speed in Venturi tube, thus less reduction in pressure and less fuel is being sucked from float chamber, however, actually if we reduce the area of the tube by closing throttle ,according to Bernoulli theorem, the speed of air in the same tube should increase, shouldn't it?
That's because it's not the restriction created by the throttle plate itself, that you see as manifold pressure (or vacuum), that is creating the suction that pulls fuel from the carburetor float bowl. It's the restriction of the venturi, where the main discharge nozzle is, which is upstream of the throttle plate. Since it's in in the upstream flow, the suction created at the venturi, being a fixed cross section, is a function of air velocity entering the carburetor, which is a function of throttle opening and engine speed.
In other words, the fuel metering system at the venturi doesn't care about the pressure differential created by the throttle plate farther down, it only cares about the velocity of the total mass flow that engine is able to pull past the venturi upstream of the throttle.
Open the throttle, the velocity of the air going through the venturi goes up, the suction generated by the venturi increases, and more fuel is pulled into the discharge nozzle. And vice versa.
In the above example of an aircraft throttle, if the throttle is closed, there will be a pressure build up below it (the far side of the engine), which will in turn suck less fuel into the mixture (low pressure differential).
If it is open, the air will flow fast, pressure will drop due to the Bernoulli principle, and more fuel will join the air.