# Air velocity in a double-skin facade

I was wondering how the air flows in a double skin facade? Say I have a glass facade with a depth of 1m, a height of 200m and a width of 10m. It is a single vertical shaft all the way up with openings at the bottom to let air in and at the top to let air out:

There is a solar radiation of 100W/m2 hitting the outside of the facade and the air velocity at ground level is 1m/s. Can I expect the velocity of the air to increase as it travels through the shaft? and to what degree?

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Yes, it may wel be possible that the fluid accelerates, this due to the expansion of the air. Suppose you have a steady state situation, then the mass flow in at the bottom (which you can calculate) should equal the mass flow rate at the top. Due to the heating, the air will expand, thus the density is decreased. As the massflow is $\int \rho v dA$, decreasing $\rho$ has to increase the velocity.

The physics behind this, includes buoyant forces due to gravity and density differences. Also, since you facade is 200m high, you should include ambient pressure difference between top and bottom (which is the reason that we have chimneys)

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