Supp. fluids problems f11

Supp. fluids problems f11 - ME 2124 Introduction to Thermal...

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ME2124 – Fall 2011 Fluid Mechanics Problems (FL) 1 ME 2124 Introduction to Thermal – Fluid Engineering Homework Problems – Fluid Mechanics – Fall 2011 1. Two plates are separated by an oil film 0.010 mm thick. Oil viscosity is μ oil = 0.1 N-sec/m 2 . The upper plate is moving at 100 mm/s. The oil flow between the plates is laminar with a li- near velocity profile (similar to Figure 1.5 in the text). What is the shear stress τ at the sur- face of the lower plate? 2. A 20 kg block and having dimensions of 0.2 m on each side slides down a 15 ° incline under its own weight. Between the bottom surface of the block and the incline is a film of oil 0.025 mm thick. The viscosity of the oil is oil = 0.1 N-sec/m 2 . a) Sketch a free-body diagram of the block showing all of the forces acting on the block and their directions. b) Find an symbolic algebraic expression for the component of the weight of the block di- rected down the incline. c) Assuming the velocity of the lubricating oil varies linearly within the small film gap, sketch the velocity profile. Assume the “no-slip” condition is satisfied at the surface of the incline and on the bottom surface of the block. d) Derive a symbolic algebraic expression for the viscous shear force acting on the block (in terms of relevant variables) and determine the direction of this force. e) Derive a symbolic algebraic solution for the velocity of the block (assuming constant velocity) as it slides down the incline. f) Determine the numerical value of velocity. If the film gap is reduced to 0.0125 mm will the velocity higher, lower, or the same? 3. The height of a fluid inside a tube or pipe can be used to measure the pressure at the base of the fluid column. An open standpipe contains 25 ° C water, with the water surface 27 m above the ground. a) What is the gage pressure at the base of this water column? b) If the column were only 2 cm high, what would the gage pressure be? 4. The difference in density between hot air and cold air results in the “chimney effect” which draws air through many heating appliances. Suppose a fireplace has a chimney that is 15 m high. The chimney is filled with air at 300 ° C. The outdoor air temperature is 0 ° C. At the top of the chimney, both the air in the chimney and the outside air are at 100 kPa. a) What is the density of the hot air leaving the chimney? b) What is the density of the cold air outside? c) Neglecting fluid friction and the change in density with eleva- tion, what is the difference in pressure between the base of the chimney ( P 1 ) and the outdoors at the same elevation ( P 2 )? 5.
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Supp. fluids problems f11 - ME 2124 Introduction to Thermal...

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