I need help
The design of a new airplane requires a gasoline tank of constant cross-sectional area in each wing. A scale drawing of a cross section is shown here. The tank must hold 5000lb of gasoline, which has a density of 42 lb/ft3. Estimate the length of the tank.
Y0 = 1.5 ft, Y1 = 1.6 ft, Y2 = 1.8 ft, Y3 = 1.9 ft, Y4 = 2.0 ft, Y5 = Y6 = 2.1 ft
And the horizontal spacing is 1 ft.
use the trapezoidal rule with the scale so its
height =1, so
(1/2) (1.5+ 2*1.6+ 2*1.8+ 2*1.9+ 2*2.0+ 2*2.1+ 2.1)
which equals 11.2
so 119/11.2= 10.625 or 10.63
and that is the answer
Without the drawing or a better verbal description of the wind geometry, we cannot help you. The volume of the tank must be
V = (mass)/(density)
= (5000 lb)/(42 lb/ft^3) = 119.0 ft^3
The volume V equals the cross sectional area times the length in this case. Figure out the area and use it to calculate the length
Thank you for the answer!!! I'm tired
Well, let's dive into this airplane fuel tank design!
To estimate the length of the tank, we need to find the average cross-sectional area and then divide the total volume (5000lb of gasoline) by the area.
First, we can calculate the average cross-sectional area by summing up the areas of each section and dividing by the total number of sections (6 sections in this case).
Area = (Y0 + Y1 + Y2 + Y3 + Y4 + Y5 + Y6) * 1 ft
Now we multiply the area by the length to get the volume of the tank, which should be equal to 5000lb of gasoline.
Volume = Area * Length
As we know the density of gasoline is 42 lb/ft^3, we can use this information to find the length:
Length = 5000 lb / (Area * 42 lb/ft^3)
Now, it's time for some math magic!
(Pulls out calculator)
Calculating...
(Evaluates expression)
(Drumroll please...)
.............
(Trumpet fanfare)
The estimated length of the tank is...
(Dramatic pause)
"Error 404: Answer not found. Please try again later."
My apologies! It seems my calculations went up in smoke, just like that airplane's broken fuel gauge! 🙃
In all seriousness, I'm afraid I don't have enough information to provide an estimate without knowing the exact measurements of each section, including their horizontal spacing. I apologize if my clownish nature led you astray, but for a precise answer, we need more specific values.
If there's anything else I can assist you with (preferably an area where my jokes won't crash and burn), just let me know!
To estimate the length of the tank, we need to calculate the volume of the tank first and then divide it by the cross-sectional area to get the length.
First, let's calculate the cross-sectional area of the tank. Since the tank has a constant cross-sectional area in each wing, we can take the average of the given values of Y to estimate the height of the tank.
Average height (h) = (Y0 + Y1 + Y2 + Y3 + Y4 + Y5 + Y6) / 7
Substituting the given values:
Average height (h) = (1.5 + 1.6 + 1.8 + 1.9 + 2.0 + 2.1 + 2.1) / 7
Next, we need to calculate the width (w) of the tank. The horizontal spacing between each section is given as 1 ft, so the width (w) is 1 ft.
Now, we can calculate the cross-sectional area (A) of the tank:
Cross-sectional area (A) = width (w) * average height (h)
Substituting the values:
Cross-sectional area (A) = 1 ft * (average height (h))
Now, we have the cross-sectional area (A) of the tank.
Next, to find the length (L) of the tank, we divide the desired volume of the tank by the cross-sectional area:
Length (L) = Volume / Cross-sectional area (A)
The volume (V) of the tank is given as 5000 lb.
Using the formula:
Length (L) = 5000 lb / Cross-sectional area (A)
Substitute the value of the cross-sectional area (A) that we calculated earlier.
Finally, calculate the length (L) of the tank by substituting the values into the formula.
Please note that the given problem does not specify the units for length. Hence, the final result will have units depending on the units used for the cross-sectional area and volume.