Aircraft’s Fuel Capacity A commercial passenger aircraft is loaded to its maximum fuel rating of 90,000 L. By using the density of 840 kg/m3 for jet fuel, calculate the fuel’s weight.

Question

Aircraft’s Fuel Capacity

A commercial passenger aircraft is loaded to its maximum fuel rating of 90,000 L. By using the density of [latex]840 kg/m^3[/latex] for jet fuel, calculate the fuel’s weight.

Approach
Since the volume and density of the jet fuel are given, we will apply Equation (6.3)

[latex]\omega [/latex]= [latex]\rho gV [/latex](6.3)

in dimensionally consistent units to calculate the weight of the fuel. The definition of the derived unit liter is listed in Table 3.2.

Table 3.2 Certain Derived Units in the SI

Quantity	SI Derived Unit	Abbreviation	Definition
Length	micrometer or micron	[latex]\mu m[/latex]	[latex]1\mu m = 10^{-6} m[/latex]
Volume	liter	L	[latex]1 L = 0.001 m^{3}[/latex]
Force	newton	N	[latex]1 N = 1 (kg . m)/s^{2}[/latex]
Torque, or moment of a force	newton-meter	N . m	—
Pressure or stress	pascal	Pa	[latex]1 Pa = 1 N/m^{2}[/latex]
Energy, work, or heat	joule	J	1 J = 1 N . m
Power	watt	W	1 W = 1 J/s
Temperature	degree Celsius	°C	°C = K – 273.15
Although a change in temperature of 1 Kelvin equals a change of 1 degree Celsius, numerical values are converted using the formula.

Accepted Answer

The fuel’s volume is first converted to the units of [latex]m^3[/latex]:

[latex] V=(90,000 L) \left(0.001\frac{m^3}{L} ight) [/latex]
[latex]=90(\cancel{L}) (\frac{ m^3}{\cancel{L}} )[/latex]
[latex]=90 m^3[/latex]

and the weight is

[latex]\omega =(840 \frac{kg}{m^3} )(9.81\frac{m}{s^2} )(90 m^3) \longleftarrow [\omega = ho gV][/latex]

[latex]=7.416 imes10^5 (\frac{ Kg}{\cancel{m^3}} )(\frac{m}{s^2} )(\cancel{m^3})[/latex]

[latex]=7.416 imes10^5\frac{kg.m}{s^2} [/latex]

[latex]=7.416 imes10^5N [/latex]

Since this numerical value has a large power-of-ten exponent, we will apply an SI prefix to represent it more compactly:

[latex]\omega =(7.416 imes 10^5 N)\left(10^{-3 }\frac{KN}{N} ight)[/latex]

[latex]=741.6(\cancel{N}) (\frac{ KN}{\cancel{N}} )[/latex]
[latex]=741.6 kN[/latex]

Discussion
To place this quantity of fuel into perspective with the USCS, the fuel weighs some 167,000 lb, or over 80 tons. Passenger aircraft typically have a fuel fraction of 25–45%, putting the takeoff weight of this aircraft between 370,000 and 670,000 lb. For example, the Boeing 767-200 aircraft holds approximately 90,000 L of fuel and has a takeoff weight of almost 400,000 lb.

[latex]\omega [/latex]= 741.6 kN

Question 6.2: Aircraft’s Fuel Capacity A commercial passenger aircraft is ...

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