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