Answer Happy

H Velocity profile measured here Figure 4: Drag Measurement. wake area }u=0 U= 35+25² }uier 4. (Bonus Question) One way to measure the drag force on an object is to measure the velocity profile in its wake. Any drag force will result in a reduction in the momentum of the fluid flowing around the object. This is the essence of conservation of momentum! Figure 4 shows an object in a flow with a free stream velocity of U = 60m/s and you experimentally measure the x component of the velocity in the wake of the object as u = 35+25r² within the range of 0 m <r <1 m. The control volume you use to analyze this flow is shown in Red lines in the figure: the outside surface of the CV follows streamlines and the front (H) has a diameter of 3 m. It looks like a cylinder that gets wider as you go to the right. If the density of the fluid is 1.23kg/m³, answer the following: (a) Explain in words why using a streamline for the top and bottom of the control volume allows us to know that the mass flux across those surfaces is zero. (b) Given that the mass flux across the streamlines is zero, find the radius of the control volume on the right hand side. i.e. determine R₂. Hint: You will need to integrate the velocity between 0 and 1 m using ring integration. (c) Determine the drag force on the object in the flow. Hint: You can not solve for the drag force directly, instead you need to add a force to the object that holds it in place. This will be equal but opposite to the drag force.