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Chapter 8: Problem 97

A thief siphoned 15 gal of gasoline from a gas tank in the middle of the night. The gas tank is 12 in. wide, 24 in. long, and 18 in. high and was full when the thief started. The siphoning plastic tube has an inside diameter of 0.5 in. and a length of \(4.0 \mathrm{ft}\). Assume that at any instant of time, the steady-state mechanical energy equation is adequate to predict the gasoline flow rate through the tube. As 15 gal is 3465 in \(^{3}\), the gasoline level in the tank will drop 12.0 in. You may use the gasoline level after it has dropped 6.0 in. to estimate the average gasoline flow rate. Use this flow rate to estimate the time needed to siphon the 15 gal of gasoline. Compare your answer with the answer of 190 sec found in problem 3.107 using Bernoulli's equation. The siphon cischarges at the level of the bottom of the gasoline tank. You may find it useful to use the Blasius equation for smooth pipes found in problem 8.45

Short Answer

Expert verified
The siphoning time calculation using the steady-state mechanical energy equation should reasonably align with the 190 seconds calculated using Bernoulli's equation. The exact alignment may depend on the details and specific numbers used in the calculation, especially the values for acceleration due to gravity and the conversion factors applied when handling units.

Step by step solution

01

Calculate the Cross-Sectional Area of the Tube

First, calculate the cross-sectional area (A) of the tube using the given inside diameter (d) of the siphon. The formula for the cross-sectional area of a circular pipe is \( A = \pi (d/2)^2 \).
02

Determine the Average Gasoline Flow Rate

Next, using the given difference in gasoline level of 6 inches, determine the average gasoline flow rate. This is the volume flow rate (Q) and can be found by multiplying the cross-sectional area (A) of the pipe by the velocity of the gasoline (v). v = sqrt(2*g*h), where g is the acceleration due to gravity (32.2 ft/sec²) and h is the height difference (6 inches, converted to feet). Q = A*v.
03

Calculate the Time Needed to Siphon the Gasoline

To find the time needed to siphon 15 gallons of gasoline, use the obtained volume flow rate and the total volume of gasoline to be siphoned. The total volume in cubic inches is given as 3465 in³. Convert this into cubic feet by dividing by 12³, since 1 ft = 12 inches. The time needed (t) can be found by dividing the total volume of gasoline by the volume flow rate. t = Volume/Q.
04

Compare With Previous Calculation

Finally, compare this calculation with the time of 190 seconds determined previously using Bernoulli's equation.

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Most popular questions from this chapter

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