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Using the Breguet range and endurance equation, estimate the amount of kerosene

love history [14]

The amount of kerosene fuel needed for an aircraft weighing 10 metric tons to fly from Boston to Los Angeles, assuming a distance of 5,000 [km] is 10000 kg.

<h3>What is Breguet equation?</h3>

Breguet equation is used to determine the range of airplane fly in some specified set of parameters.

$R=\dfrac{h_f}{g}\dfrac{L}{D}\times \eta \ln \left(\dfrac{W_{initial}}{W_{final}}\right)$

Here, (L/D) is lift to drag ratio,<em> g</em> is gravitation acceleration,<em> h </em>is height and <em>W</em> is weight.

The weight of aircraft is 10 metric tons (this is the dry weight that includes passengers and cargo) The distance of 5,000 [km], with velocity at 300 [m/s] from Boston to Los Angeles has to be cover by the airplane.

The initial weight is 10 metric tons or 10000 kg. Thus, the final weight with total fuel burn is,

$W_{final}=W_{initial}-W_{fuel}\\W_{final}=1-\dfrac{W_{fule}}{W_{initial}}$

The lift-to-drag ratio is 15 and the overall efficiency is 0.3, The standard air density at an altitude of approximately 6,000 [m] is half.

Thus, put the values, in above formula,

$5000=\dfrac{6000}{9.81}(15)\times(0.3) \ln \left(\dfrac{10000}{1-\dfrac{W_{fuel}}{10000}}}\right)\\$

$\ln \left(\dfrac{10000}{1-\dfrac{W_{fuel}}{10000}}}\right)=1.8167\\\ln \left(\dfrac{1}{10000-W_{fuel}}}\right)=1.8167$

Solving this equation, we get,

$W_{fuel}=10000\rm\; kg\\$

Thus, the amount of kerosene fuel needed for an aircraft weighing 10 metric tons to fly from Boston to Los Angeles, assuming a distance of 5,000 [km] is 10000 kg.

Learn more about the Breguet equation here:

brainly.com/question/15218094

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