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ME 471 - Midterm Exam 1 Solutions

It may be assumed that the dynamic viscosity and the

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Unformatted text preview: he dynamic viscosity and the speed of sound are related to the temperature as follows: From ideal gas equation, we have: √ √ √ *( )*( *( )* 4) Draw a neat labelled graph showing the variation of aerodynamic efficiency ( with angle of attack . ratio) 5) Draw a labelled graph showing the variation of with aerofoil thickness (in percent chord) for two cases of non-identical Reynolds numbers ( varies from to ). 6) Explain in a couple of sentences why the tips of some airplane wings are bent upward. Wingtip devices are usually intended to improve the efficiency of fixed-wing aircraft. Wingtip devices increase the lift generated at the wingtip (by smoothing the airflow across the upper wing near the tip) and reduce the lift-induced drag (or downwash) caused by wingtip vortices, improving lift-to-drag ratio. 7) Plot the variation of drag coefficient with Reynolds number speed flow ( varies from to ). 8) For an airfoil having chord length and for a sphere in low- with moment values per unit span as ; calculate the location of center of pressure. Using Equation 1.22 from the textbook / formula sheet (or refer Example 1.4): This gives: 9) In a couple of sentences, explain the Buckingham Pi Theorem. If there is a physically meaningful equation involving a certain number, n, of physical variables, and k is the number of fundamental dimensions; then the original expression is equivalent to an equation involving a set of p = n − k dimensionless parameters constructed from the original variables. The Buckingham π theorem provides a method for computing sets of dimensionless parameters from the given variables, even if the form of the equation is still unknown; even though the choice of dimensionless parameters is not unique. 10) On a single, clearly la...
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