An incompressible fluid flows in a duct of radius \(r_{0}\). At a particular location, the velocity distribution is \(u=U_{m}\left[1-\left(r / r_{0}\right)^{2}\right]\) and the distribution of an extensive property is \(\beta=B_{m}\left[1-\left(r / r_{0}\right)\right]\). Evaluate the integral \(\int ho \beta(\mathbf{V} \cdot \hat{n}) d A\) at this location.