$$p_v = \frac{1}{2}\rho V^2$$

Where:

- \(p_v\) is the velocity pressure (in Pa)

- \(\rho\) is the density of the air (in kg/m^3)

- \(V\) is the velocity of the air (in m/s)

We can rearrange this equation to solve for the velocity:

$$V = \sqrt{\frac{2p_v}{\rho}}$$

Substituting the given values, we get:

$$V = \sqrt{\frac{2(0.20\text{ in w.g.})(47.88\text{ Pa/in w.g.})}{1.225\text{ kg/m}^3}} = 4.04\text{ m/s}$$

Therefore, the air moves through the round duct at a velocity of \(4.04 \text{ m/s}\).