system
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human
What is the maximum theoretical efficiency of an air turbine and how close can we get to it with current technology?

The maximum theoretical efficiency of an open air wind turbine is defined by Betz's law to be 59.3%. But if instead the turbine was inside a circular tube of constant diameter, and had a pressure drop of so many pascals across it, how would an ideal turbine behave? As in what would the air flow rate through it be, and how much energy would it extract from this flow? (Given a certian air density) How close can current technology get to that figure? 

edit:

This is in the context of a solar updraught tower. There is negative pressure at the bottom of the tower due to the buoyancy of hot air in the tower (stack effect) compared to outside. If there were a turbine in the tower, how much energy could it generate?

My situation is as follows: the tower is 20m diamater. The negative pressure generated by the stack effect is 630Pa. If there were no obstructions in the tower, roughly 7500 cubic metres of air per second will flow up the tower. Since the air density is 0.938 kg/m3 and the air is rising at 24 ms^-1 , one cubic metre of air will have the kinetic energy of 270J. There are 7500 of these per second, so the total kinetic power is about 2*10^6 watts.

That is for an open tube with no restrictions. A turbine will act as a restriction for the air (like a resistor in an electrical circuit), so the flow rate will be lower. I was just wondering if there was a rule-of-thumb equation or number concerning the flow rate through an ideal turbine given a pressure difference (or how much it will impede the air flow stated above), and how much energy will be captured by it.

By "efficiency" I mean the proportion of the kinetic energy in the rising air captured by the turbine.
gpt
Modern multiple stage bladed turbines typically reach 60–70% efficiency, while large steam turbines often show turbine efficiency of over 90% in practice. Volute rotor matched Tesla-type machines of reasonable size with common fluids (steam, gas, and water) would also be expected to show efficiencies in the vicinity of 60–70% and possibly higher.