Øving 1TEP4100 Fluidmekanikk, V̊ar 2013

1-52 Consider the flow of air through a wind turbine whose blades sweep an area of diameterD (in m). The average air velocity through the swept area is V (in m/s). On the bases of theunits of the quantities involved, show that the mass flow rate of air (in kg/s) through the sweptarea is proportional to air density, the wind velocity, and the square of the diameter of the sweptarea.

1-56 The drag force exerted on a car by air depends on a dimensionless drag coefficient, the den-sity of air, the car velocity, and the frontal area of the car. That is, FD = function(Cdrag,Afront, ρ,V).Based on unit considerations alone, obtain a relation for the drag force.

2-12 The pressure in an automobile tire depends onon the temperature of the air in the tire. When the air temper-ature is 25◦C, the pressure gage reads 210kPa. If the volume ofthe tire is 0.025m3, determine the pressure rise in the tire whenthe air temperature in the tire rises to 50◦C. Also, determinethe amount of air that must be bled off to restore the pressure toits original value at this temperature. Assume the atmosphericpressure to be 100kPa.

Additional MatLab assignmentDuring a drive the temperature of the air inside the tire will change due to the varying speed ofthe vehicle, the sun heating the tire, cooling air, etc. During a certain drive, the temperature isregistered at seven measurements at different times to be 25◦C, 43◦C, 57◦C, 21◦C, 32◦C, 43◦C

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and 50◦C. Find the air pressure at these temperatures, and determine the amounts of air thatmust be bled off to restore the pressure to its original value at these temperatures. A singlestatement is to be used to find the masses corresponding to the new temperatures, but at theoriginal pressure (meaning only one command should be used to compute those masses, no loopshould be used). Finally, plot the calculated masses of released air. Print the plot and hand itin with the rest of your answer for the assignment.

2-20 In a piping system, the water temperature remains under 35◦C. Determine the minimumpressure allowed in the system to avoid cavitation.

2-70 A 50cmx30cmx20cm block weighing 150N is to be moved at a constant velocity of 0.8m/son an inclined surface with a friction coefficient of 0.27.

(a) Determine the force F that needs to be applied in the horizontal direction.(b) If a 0.4mm thick oil film with a dynamic viscosity of 0.012Pa · s is applied

between the block and inclined surface, determine the percent reduction inthe required force.

2-99 Contrary to what you might expect, a solid steel ball can float on water due to thesurface tension effect. Determine the maximum diameter of a steel ball that would float onwater at 20◦C. What would your answer be for an aluminum ball? Take the densities of steeland aluminum balls to be 7800kg/m3 and 2700kg/m3, respectively.

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