Question

Problem 3. (30 points) From inviscid potential flow analysis, as a uniform stream approaches a cylinder of radius R along the symmetry line AB in the figure, the velocity has only one component: u(x)=U_{\infty}\left(1-\frac{R^{2}}{x^{2}}\right) \text { for }-\infty<x \leq-R \text { where } U_{\infty} \text { is the stream velocity far from the } a. Using EXCEL, plot u(x) along AB from -0.4<x<-0.05 when R=0.05 m and U,=4 m/s.Label axes with variables and dimensions and add a title to the plot. Since the solution is analytical, it should be plotted using a smooth curve and no symbols.Include enough points in your spreadsheet to resolve the curve. \text { Find the acceleration } \mathbf{a}_{\mathbf{x}}=\frac{\mathbf{D u}}{\mathbf{D t}} \text { along } \mathbf{A B} \text { as a function of } U_{\infty}, \mathbf{R} \text { and } \mathbf{x} \text { . } Using EXCEL, plot du/dt from -0.4 x0.05 when r=0.05 and u= 4m/s axes with variables and dimensions and add a title to the plot. Since the solution is analytical, it should be plotted using a smooth curve and no symbols. Include enough points in your spreadsheet to resolve the curve. Find the maximum flow deceleration along AB and its location when R=0.05 m and U=4 m/s. (Partial answer: Xmin= -0.0646 m)  Fig: 1  Fig: 2  Fig: 3  Fig: 4  Fig: 5  Fig: 6  Fig: 7