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100S11_PS2 Soln

# 100S11_PS2 Soln - ENES 100 Introduction to Engineering...

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ENES 100 Introduction to Engineering Design Spring 2011 1/6 Problem Set #2 SOLUTIONS Assigned: Feb. 4, 2011 Due: In class on Feb. 14 (M) or Feb. 15 (Tu) Reading: Chapter 3: Fluid Mechanics and Design Analysis Chapter 7: Computer Aided Design (CAD) Assume the air density to be ρ =1.2 kg/m 3 , and the acceleration of gravity g=9.8 m/s 2 for all problems. Show all calculations where necessary. To receive full credit, you must show and explain your calculations. Problems: 1. For this problem, you are tasked with performing a study showing the effects of hover height and power on the selection of your levitation fan. Note: Microsoft Excel can be used for this assignment (recommended), please pay close attention to significant figures, round up or down as necessary . (a) Consider a circular hovercraft 0.40 m in diameter with a mass of 2.5 kg set to levitate at 1.0mm, 2.0mm and 3.0mm hover heights. Calculate the Δ p and Q that the levitation fan provides for this hovercraft for each hover height. Similarly to vehicle geometry and mass, hover height is also a design parameter. Discuss how the increase in hover height from 1 to 3 mm changes the Δ p and Q requirement for your levitation fan. Planform area: 2 2 13 . 0 ) 20 . 0 )( 14 . 3 ( * m m r A = = = π Perimeter: m r 3 . 1 2 = = π l Levitation pressure: ( ) ( ) 2 2 2 190 13 . 0 8 . 9 5 . 2 m N m s m kg A Mg p = = = Δ NOTE: The pressure necessary to levitate is the same independent of gap height ( )( ) ( ) min 38 . 1 023 . 0 2 . 1 190 2 3 . 1 001 . 0 2 3 3 3 2 m s m m kg m N m m p h Q = = = Δ = ρ l (1mm) ( )( ) ( ) min 76 . 2 046 . 0 2 . 1 190 2 3 . 1 002 . 0 2 3 3 3 2 m s m m kg m N m m p h Q = = = Δ = ρ l (2mm)

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ENES 100 Introduction to Engineering Design Spring 2011 2/6 ( )( ) ( ) min 14 . 4 069 . 0 2 . 1 190 2 3 . 1 003 . 0 2 3 3 3 2 m s m m kg m N m m p h Q = = = Δ = ρ l (3mm) Note: not necessary to convert to m 3 /min, answers in m 3 /s acceptable. The volumetric flowrate Q linearly increases with increase in gap height h. The Q requirement for the fan doubles from 1.0mm to 2.0mm and then triples from 1.0mm to 3.0mm. (b) Using the power equation P = Δ pQ, calculate the power required to hover at 1.0, 2.0, and 3.0 mm hover heights. Power required for Q 1 , Q 2 , Q 3 & Δ p: Δ p is the same for all 3 hover heights, therefore, only the Q values change.
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100S11_PS2 Soln - ENES 100 Introduction to Engineering...

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