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A 50 cm diameter pipe carries water (v = 0.294 × 10–6 m2/s) at an average velocity of 10 m/s . The roughness of pipe surface is 0.8 mm. For fully rough turbulent flow, What is the boundary shear stress.
  • a)
    275
  • b)
    277
Correct answer is between '275,277'. Can you explain this answer?
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A 50 cm diameter pipe carries water (v = 0.294 × 10–6 m2/s) at an ave...
F = 0.022
Shear velocity
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A 50 cm diameter pipe carries water (v = 0.294 × 10–6 m2/s) at an ave...
To calculate the boundary shear stress for fully rough turbulent flow in a pipe, we can use the Darcy-Weisbach equation:

𝑓 = (1/√𝑓) + 2 log10((𝜖/𝑅)√𝑓)

Where:
𝑓 = Darcy-Weisbach friction factor
𝜖 = roughness height on the pipe surface
𝑅 = hydraulic radius of the pipe

In this case, we are given the diameter of the pipe, so we can calculate the hydraulic radius:

𝑅 = 𝐷/4 = 50 cm / 4 = 12.5 cm = 0.125 m

Given that the roughness height is 0.8 mm, we need to convert it to meters:

𝜖 = 0.8 mm = 0.8 × 10^(-3) m

Now we can solve the Darcy-Weisbach equation for the friction factor. Since this is fully rough turbulent flow, we assume the friction factor is constant:

𝑓 = 0.02

Next, we can use the friction factor to calculate the boundary shear stress using the following equation:

𝜏 = 𝑓 × (𝜌 × 𝑢^2)/2

Where:
𝜏 = boundary shear stress
𝜌 = density of water
𝑢 = average velocity of water in the pipe

Given that the average velocity is 10 m/s and the density of water is approximately 1000 kg/m^3, we can substitute these values into the equation:

𝜏 = 0.02 × (1000 kg/m^3 × (10 m/s)^2)/2 = 0.02 × 5000 N/m^2 = 100 N/m^2

Converting to Pascal (Pa), we get:

𝜏 = 100 Pa

This is equivalent to 100 N/m^2, and since 1 N/m^2 is equal to 1 Pascal, the boundary shear stress is 100 Pa.

Therefore, the correct answer is not between 275 and 277. The correct answer is 100 Pa.
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A 50 cm diameter pipe carries water (v = 0.294 × 10–6 m2/s) at an average velocity of 10 m/s . The roughness of pipe surface is 0.8 mm. For fully rough turbulent flow, What is the boundary shear stress.a)275b)277Correct answer is between '275,277'. Can you explain this answer?
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