The figure below shows the time-average velocity profiles measured upstream and downstream of a cylinder in...

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The figure below shows the time-average velocity profiles measured upstream and downstream of a cylinder in an unconfined, incompressible flow that has a free-stream velocity Uo. The wake appears as a linear variation of x-velocity, u, from 0 to Uo going from y= 0 to ±2D. Using integral analysis with conservation of mass and momentum, we wish to determine the drag on the cylinder (assume infinitely long). Note: At the upstream and downstream boundaries, the flow is aligned with the x-coordinate (v~ 0). a) (10 points) Using CV 1, determine the drag force per unit length on the cylinder. CV 1 is bound by a streamline on the top and bottom. Hint: flow does not cross streamlines. b) (10 points) Using CV 2, the rectangle, determine the drag force per unit length on the cylinder. Hint: Flow crosses the top and bottom boundaries and u >> v and u U。 at these boundaries. 2 CV 1, Streamline и U Streamlines y U₁ CV 2, Rectangle น - U ~ 0 2D Wake zone 2D U₁ The figure below shows the time-average velocity profiles measured upstream and downstream of a cylinder in an unconfined, incompressible flow that has a free-stream velocity Uo. The wake appears as a linear variation of x-velocity, u, from 0 to Uo going from y= 0 to ±2D. Using integral analysis with conservation of mass and momentum, we wish to determine the drag on the cylinder (assume infinitely long). Note: At the upstream and downstream boundaries, the flow is aligned with the x-coordinate (v~ 0). a) (10 points) Using CV 1, determine the drag force per unit length on the cylinder. CV 1 is bound by a streamline on the top and bottom. Hint: flow does not cross streamlines. b) (10 points) Using CV 2, the rectangle, determine the drag force per unit length on the cylinder. Hint: Flow crosses the top and bottom boundaries and u >> v and u U。 at these boundaries. 2 CV 1, Streamline и U Streamlines y U₁ CV 2, Rectangle น - U ~ 0 2D Wake zone 2D U₁