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ENES100_PS2_solutions_S09

ENES100_PS2_solutions_S09 - ENES 100 Problem Set 2 Spring...

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ENES 100 Problem Set 2 Spring 2009 1 ENES 100 Introduction to Engineering Design Problem Set 2: Fluid Mechanics of Fans Spring 2009 Prepared by Evandro Valente Assigned: 2/6 Due Date: In class on 2/16 (M) or 2/17 (Tu) Reading: Chapter 3 of Introduction to Engineering Design 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. Assume the air density to be ρ =1.2 kg/m 3 , and the acceleration of gravity g=9.8 m/s 2 . 1a) For your baseline parameter, consider a circular hovercraft 0.5 m in diameter weighing 2 kg set to perform at 1mm hover height. Calculate Δ p and Q for the baseline parameters above and hover heights of 2mm and 3mm. Similarly to vehicle dimension and weight, hover height is also a target parameter set by the designers, discus how the increase in hover height changes the requirement ( Δ p and Q) for your levitation fan. Planform area: Perimeter: Levitation pressure: NOTE: Pressure needed to lift the vehicle DOES NOT vary with change in levitation height! Flow Rate for 1mm, 2mm & 3mm (1mm) (2mm) (3mm) Changing the hover height does not change the levitation pressure, because gap height is not a parameter in the Δ p equation. However, the volumetric flowrate Q linearly increases with increase in gap height h. The Q requirement doubles from

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ENES 100 Problem Set 2 Spring 2009 2 1mm to 2mm and then triples from 1mm to 3mm. 1b) Using the power equation P = Δ pQ, find the various power values associated with the 1, 2, and 3 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. 1c) For your baseline parameter, consider a circular hovercraft 0.5 m in diameter weighing 2 kg set to perform at 1mm hover height (same as 1a). Calculate Δ p and Q for the baseline parameters above and also for the following vehicle weights: 2.2kg, 2.4kg, 2.6 kg, 2.8 kg and 3.0 kg. Similarly to vehicle dimension and hover height,
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