Problem

An intubed fan (a fan rotating within a tube or other conduit) is mounted on a cart that i...

An intubed fan (a fan rotating within a tube or other conduit) is mounted on a cart that is connected to a fixed wall via a linear elastic spring with constant k = 70 N/m. Assume that in a particular test the fan draws air that enters the tube at A with a speed υA. The outgoing flow at B has a speed υB. The flow of air through the tube causes the cart to displace to the left so that the spring is stretched by 0.25 m from its unstretched position. Assume that the density of air is constant throughout the tube and equal to ρ = 1.25 kg/m3. In addition let the tube’s cross section be circular, and let the cross-sectional diameters at A and B be dA= 3 m and d = 1.5 m, respectively. Determine the velocities of the airflow at A and B.