Venturi tube obeys ideal gas law?

[parislad]

The ideal gas law staes that pressure is inversely proportional to volume. Makes sense but I am confused by what happens in a venturi tube, where volume seems to decrease at the same time that pressure decreases also. I understand that dynamic pressure increases in the throat but what am I missing...
Is it something to do with the fact that the tube is not strictly a contained volume?
Any good explanation to clear my mind would be appreciated, thanks.

 

[rcgldr]

In an ideal situation, the Venturi tube has no friction with the air and doesn't apply any force in the direction of flow, and the air isn't compressable or expandable. Mass flow across any cross section of the Venturi tube is constant (even in the real world, except during transitions of the input speed). Since the air isn't compressable or expandable in the ideal case, then the velocity is inversely proportional to the cross sectional area since mass flow is constant. This means that velocity is greater in the narrower section of the venturi. Since in the ideal case the Venturi doesn't apply any force in the direction of flow the only source of the acceleration responsible for the change in velocity versus cross sectional area must be due to a pressure differential within the air itself. This means that the pressure is less in the narrower sections of the venturi and that the air is moving faster.

This is an idealized case. In the real world, a pipe opposes any relative flow and although mass flow remains constant, the pressure of the flow is reduced as a gas or fluid travel through a pipe even in a constant diameter pipe.

 

[russ_watters]

The decreasing pipe diameter does not imply a decreasing volume. In fact, the ideal gas law could be seen as an explanation of why the velocity has to increase: the area decreases while the volume does not.

Note also at low speed the pressure change is too small to notice a volume change vs the venturi effect itself. The volume is assumed to be constant.