Fluid Mechanics: Cross Sectional Area of Gas Tank?

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SUMMARY

The discussion focuses on calculating the cross-sectional area of a gas tank given the inflow rate of 5.3 gallons per minute and the rise in gas level at 4.3 inches per minute. The user attempted to derive the area using the volume formula A = L*W and the relationship between volume and height, but encountered inconsistencies in their calculations. The correct approach involves recognizing that the volume flow rate (Q) can be expressed as Q = A * V, where V is the velocity of the gas rising in the tank. Understanding the relationship between these variables is crucial for accurate calculations.

PREREQUISITES
  • Understanding of fluid mechanics principles, specifically flow rates.
  • Familiarity with volume calculations in geometry, particularly A = L*W.
  • Knowledge of the relationship between flow rate, cross-sectional area, and velocity (Q = A * V).
  • Basic grasp of units conversion, particularly between gallons and cubic inches.
NEXT STEPS
  • Research the principles of fluid dynamics, focusing on flow rates and cross-sectional area calculations.
  • Study the conversion between gallons and cubic inches to ensure accurate volume measurements.
  • Learn about control volumes and their applications in fluid mechanics.
  • Explore practical examples of calculating cross-sectional areas for various tank shapes.
USEFUL FOR

Students studying fluid mechanics, engineers involved in tank design, and anyone interested in understanding fluid flow and volume calculations.

dmalwcc89
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Homework Statement



Gas pours into your gas tank at 5.3 gallons per minute.
You can't see it, but the gas level inside the tank rises at 4.3 inches per minute.

What is the cross sectional Area of the gas tank?
Is this realistic?

Homework Equations



I'm not sure what shape the tank is, but A = L*W, V = L*W*H

The Attempt at a Solution



I tried solving A by saying after one minute, there is 5.3 gallons in the tank = V. Then, H would be 4.3 at that instant, and this would give me A. But I get a 1.23 in value which makes no sense. Just to gauge where I am at in this class, we are beginning control volumes and in/out flows. So we're using equations that have to do with V(dot)A, where V is velocity. But this problem only has one inlet, so I'm not sure if that applies here.
 
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What about Q = A V
and calculate A?!

Thanks,
 
Just remember the gallons is a volume measurement, so you just need to think about the units and solve for cross sectional area.
 

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