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# Examples - AE 312 EXAMPLES 1 J C Dutton In an experiment to...

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1 AE 312 EXAMPLES J. C. Dutton 1. In an experiment to determine drag, a circular cylinder of diameter d was immersed in a steady, two-dimensional, incompressible flow. Measurements of velocity and pressure were made at the boundaries of the control surface shown. The pressure was found to be uniform over the entire control surface. The x-component of velocity at the control surface boundary was approximately as indicated by the sketch. From the measured data, calculate the drag coefficient of the cylinder based on the projected area and on the freestream dynamic head, 2 0 V 2 / 1 ρ . d V 2 1 Length Unit per Force Drag C 2 0 D ρ = 2. Air is expanded isentropically in a horizontal nozzle from an initial pressure of 1.0 MPa and initial temperature of 800 K to an exhaust pressure of 101 kPa. If the air enters the nozzle with a velocity of 100 m/s, determine the air exhaust velocity. Assume the air behaves as a perfect gas, with R = 287 J/kg·K and γ = 1.4. Repeat for a vertical nozzle with exhaust plane 2.0 m above the intake. 3. A normal shock wave occurs at the inlet to a diverging section as shown. The area ratio A b /A a is equal to 3.0. Find the Mach number and static pressure immediately behind the shock and the loss in stagnation pressure across the shock. Repeat for a shock at the exit. psia 2 P 5 . 2 M = = a b Normal shock psia 2 P 5 . 2 M = = a b Normal shock

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2 4. For the air hammer problem, assume V U = 500 ft/s, T U = 70°F, and P U = 14.7 psia. Calculate the static pressure and temperature behind the wave and the velocity of the wave relative to the pipe walls. Also, find the stagnation pressure and stagnation temperature on both sides of the shock relative to both the wave and to the pipe walls.
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