Oil with a density of 850 kg/m3 and viscosity of 0.527 kg/ms is being discharged by a 8-mm-diameter, 40-m-long horizontal pipe from a storage tank open to the atmosphere. The height of the liquid level above the center of the pipe is 4 m. Disregarding the minor losses, determine the Fanning friction factor of the pipe flow.
Question
Oil with a density of 850 kg/m3 and viscosity of 0.527 kg/ms is being discharged by a 8-mm-diameter, 40-m-long horizontal pipe from a storage tank open to the atmosphere. The height of the liquid level above the center of the pipe is 4 m. Disregarding the minor losses, determine the Fanning friction factor of the pipe flow.
Solution
The Fanning friction factor can be determined using the Darcy-Weisbach equation, which relates the head loss due to friction (hf) in a pipe to the friction factor (f), the length of the pipe (L), the velocity of the fluid (V), the diameter of the pipe (D), and the acceleration due to gravity (g). The equation is:
hf = 4f * (L/D) * (V^2 / 2g)
We can rearrange this equation to solve for the friction factor:
f = hf / [4 * (L/D) * (V^2 / 2g)]
Step 1: Calculate the velocity of the fluid. The velocity can be determined using Torricelli's theorem, which states that the speed of efflux (V) from a hole under a fluid of height h is given by:
V = sqrt(2gh)
where g is the acceleration due to gravity. Take g to be 9.81 m/s².
V = sqrt(2 * 9.81 m/s² * 4 m) = 8.85 m/s
Step 2: Calculate the head loss due to friction. The head loss is equal to the height of the liquid level above the center of the pipe, which is 4 m.
hf = 4 m
Step 3: Substitute the known values into the equation for the friction factor:
f = 4 m / [4 * (40 m / 0.008 m) * (8.85 m/s)^2 / (2 * 9.81 m/s²)] = 0.022
So, the Fanning friction factor of the pipe flow is approximately 0.022.
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