Problem 3: Bernoulli The Quonset hut is a lightweight structure with a half-cylindrical cross section and a length that extends into the page (Fig 3). The flow over a Quonset hut may be approximated by the velocity field assuming steady, frictionless, and incompressible flow: =U (1- (2)²) cos(0)êr - U U (1+ (²)²) si V = sin(0)êe. U Рос R Figure 3: Flow over a Quonset hut. (1) Obtain an expression for the pressure distribution P(0) along the surface of the hut (r = a). (2) During a wind storm, the wind speed is at 28 m/s and the static air pressure is 96 kPa. The air pressure inside the hut is the same as the outside static pressure. The hut has a diameter of 6 m and a length of 18 m. Take the density of the air to be 1.22 Kg/m³. Using the equation derived, find the net vertical force on the Quonset hut resulting from the pressure difference between the inside and outside of the hut. (3) What is the pressure distribution between the front (0 = 180°) and the back (0 = 0°). Explain the consequence of your result in terms of the net horizontal force (drag force) and whether the result is physical.