Gasoline assume octane flows at a rate of 4 ins in a 38 in d

Gasoline (assume octane) flows at a rate of 4 in./s in a 3/8 in. diameter fuel line of an automobile. The flow is modeled with water flowing in a 1 in. ID pipe. What is the corresponding water velocity in the water pipe? Assuming that the pressure drop in the water pipe is 4.5 psi, determine the pressure drop in the fuel line.

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Solution

Reynold number of both flows must be same

assuming kinematic viscoity of octane as 8.05 * 10^-7 m^2/s and water as 10^-6 m^2/s

V_gas * D_gas / nu_gas   = V_water * D_water / nu_water

4 * 3 / 8 * 8.05*10^-7   = V * 1 * / 1*10^-6

V = 1.86335 in/s

pressure drop in water pipe = k * V_water ^2   = k * 1.86335^2 = 4.5

k = 1.29605

pressure drop in gasoline pipe = 1.29605 * V_gas^2   = k * 9/64 = 0.1822 psi