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Automobile Pump Power

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Gasoline is pumped from the gas tank of an automobile to the carburetor through a 10 ft long, 1/4" diameter fuel line of steel tubing. The line has five 90 degree smooth bends with r/d of 6. The gasoline discharges through a 1/32" diameter jet in the carburetor to a pressure of 14 psia. The pressure in the tank is 14.7 psia. If the pump is 80% efficient, what power must be supplied by the pump if the automobile is accelerating and consuming fuel at the rate of 0.1 gal/min.?

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The frictionless flow energy equation states the sum of energies at any point on the flow energy line should be constant.

Therefore

Pressure energy + kinetic energy + potential energy = constant
Pressure energy = static Pressure / density
Kinetic energy = half of Square of velocity
Potential energy = static head x gravitational acceleration

Then applying this to carburetor tube:

Pressure/density + V^2/2 + gZ = constant across any point on the gasoline feed line

Applying the energy equation between points 1 and 2 on the energy line yields:
P1/density1 + 1/2 (V1)^2 + gZ1 = P1/density1 + 1/2 (V1)^2 + gZ1 ----- (1)

If the flow experiences some pipe friction losses and energy added to the flow from the fuel pump the above equation could be written as:
P1/density + 1/2 (V1)^2 + gZ1 = P2/density1+ 1/2 (V2)^2 + gZ2 + pipe friction and secondary energy losses - fuel pump energy ------ ...

Solution Summary

The frictionless flow energy equation states the sum of energies at any point on the flow energy line should be constant. This solution provides calculations and is 575 words.

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JENN Inc. supplies under-hood emission control air pumps to the automotive industry. The pump is vacuum-powered and works while the engine is operating., cleaning the exhaust by pumping extra oxygen into the exhaust system. If a pump fails before the vehicle in which it is installed has travelled 50,000 miles, Federal emission regulations require that it be replaced at no cost to the vehicle owner. The company's current air pump lasts an average of 61,000 miles, with a standard deviation of 9,000 miles. The number of miles a pump operates before becoming ineffective has been found to follow a Normal distribution.

1. For the current pump design, what percentage of the company's pumps will have to be replaced at no charge to the vehicle owner? (show analysis for practice prob and show why)

2. What percentage of the company's pumps will fail at exactly 50,000 miles? (show analysis and why)

3. What percentage of the company's pumps will fail at mileage between 42,000 and 57,000 ? (show work/why)

4. For what number of miles does the probability become 80% that a randomly selected pump will no longer be effective? (show how assessed/why)

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