ME313 Flow of Compressible Fluids s1

ME3251 Flow of Compressible Fluids Spring 2013 Dr. T. J. Barber

Problem Set 2: Control Volumes

Problem 4

In an experiment to determine the drag force on a body, a circular cylinder of diameter D was immersed in a steady, two-dimensional, incompressible flow. Measurements of the velocity and pressure were made at the boundaries of the control surface shown in the figure below. The pressure was found to be uniform over the entire control surface. The x-component of the velocity at the control surface boundary was approximately as indi- cated by the sketch.

From the measured data, show that the drag coefficient of the cylinder, based on the projected or frontal area and on the freestream dynamic head is: Drag 4 C   D 1 V2 D 3 2

U Control Surface U  

Problem 5

Determine the force F required to push the flat plate of Figure below against the round air jet with a velocity of 10 cm/s. The air jet velocity is 100 cm/s, with a jet diameter of 5.0 cm. Air density is 1.2 kg/m3. Problem 6

Air enters a hand held hair dryer with a velocity of 3 m/s at a temperature of 20°C and a pressure of 101 kPa. Internal resistance heaters warm the air and it exits through an area of 20 cm2 with a velocity of 10 m/s at a temperature of 80°C. Assume that internal obstructions do not appreciably affect the pressure between inlet and exit and that heat transfer to the surroundings are negligible. Determine the power in kW needed to operate the hair dryer at steady state.