Automotive Fuel Line
An automobile is driving at 40 mph, and it has a fuel economy rating of 28 miles per gallon. The fuel line from the tank to the engine has an inside diameter of \frac{3}{8}in.(a) Determine the volumetric flow rate of fuel in units of ft^3/s. (b) In the dimensions of in./s, what is the gasoline’s average velocity? (c) What is the Reynolds number for this flow?
Approach
We can use the given information for the automobile’s speed and fuel economy rating to find the volumetric rate at which gasoline is consumed. Then, knowing the cross-sectional area of the fuel line [Equation (5.1)],
A=\pi \frac{d^{2} }{4} (5.1)
we will apply Equation (6.10)
q=Av _{avg} (6.10)
to determine the flow’s average velocity. Lastly, we calculate the Reynolds number using Equation (6.6),
R{e}=\frac{\rho vl}{\mu } (6.6)
where the characteristic length is the fuel line’s diameter. The density and viscosity of gasoline are listed in Table 6.1.
Table 6.1 Density and Viscosity Values for Several Gases and Liquids at Room Temperature and Pressure
| Density,ρ | Viscosity, μ | |||
| Fluid | kg/m^3 | slug/ft^3 | kg/(m . s) | slug/(ft . s) |
| Air | 1.20 | 2.33×10^{-3} | 1.8×10^{-5} | 3.8×10^{-7} |
| Helium | 0.182 | 5.53×10^{-4} | 1.9×10^{-5} | 4.1×10^{-7} |
| Freshwater | 1000 | 1.94 | 1.0×10^{-3} | 2.1×10^{-5} |
| Seawater | 1026 | 1.99 | 1.2×10^{-3} | 2.5×10^{-5} |
| Gasoline | 680 | 1.32 | 2.9×10^{-4} | 6.1×10^{-6} |
| SAE 30 oil | 917 | 1.78 | 0.26 | 5.4×10^{-3} |
