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An unloaded helicopter of mass 10,000 kg hovers at sea

Fluid Mechanics | 2nd Edition | ISBN: 9780071284219 | Authors: Yunus A. Cengel, John M. Cimbala ISBN: 9780071284219 39

Solution for problem 33P Chapter 6

Fluid Mechanics | 2nd Edition

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Fluid Mechanics | 2nd Edition | ISBN: 9780071284219 | Authors: Yunus A. Cengel, John M. Cimbala

Fluid Mechanics | 2nd Edition

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Problem 33P

Problem 33P

An unloaded helicopter of mass 10,000 kg hovers at sea level while it is being loaded. In the unloaded hover mode, the blades rotate at 400 rpm. The horizontal blades above the helicopter cause a 18-m-diameter air mass to move downward at an average velocity proportional to the overhead blade rotational velocity (rpm). A load of 14,000 kg is loaded onto the helicopter, and the helicopter slowly rises. Determine (a) the volumetric airflow rate downdraft that the helicopter generates during unloaded hover and the required power input and (b) the rpm of the helicopter blades to hover with the 14,000-kg load and the required power input. Take the density of atmospheric air to be  1.18 kg/m3. Assume air approaches the blades from the top through a large area with negligible velocity and air is forced by the blades to move down with a uniform  velocity through an imaginary cylinder whose base is the blade span area.

Step-by-Step Solution:
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• SpeedingUpIndex o Somethingpersomethingelse=index o something/somethingelse=speed/time=acceleration • Tofindacceleration…(twoways) 1. DataTableWay Example: t v Δt(t 2t 1) Δv(v 2v )1 a(Δv/Δt) 0s 5mph -- -- -- 2s 25mph 2 20 10 4s 45mph 2 20 10 2. AccelerationEquation:(a)=Δv/Δt (0s,5mph) (4s,45mph) a=Δv/Δt=(45mph-5mph)/(4s-0s)=40mph/4s=10mph/s v=v 0+at v 0=v–at a=v–v /0 t=v–v /0 Example#1:Ifat0seconds,atruckismovingat10mphandisat30mph10secondslater, whatistheaccelerationofthecar a=v 1–v /0 v 0=10mph v 1=30mph a=30mph–10mph/10s-0s t0=0s t1=10s a=20mph/10s a=2mph/s Example#2:Acarstartsat5mphandacceleratesatarateof3mph/s.Howlongdoesittake togetat30mph t=v–v 0aàt=(30mph-5mph)/(3mph/s)=25/3=8.33seconds • “Falling” o velocity

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Chapter 6, Problem 33P is Solved
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Textbook: Fluid Mechanics
Edition: 2
Author: Yunus A. Cengel, John M. Cimbala
ISBN: 9780071284219

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An unloaded helicopter of mass 10,000 kg hovers at sea