The Colebrook equation is given by \[ \frac{1}{\sqrt{f}}=-0.86 \ln \left(\frac{\epsilon / D}{3.7}+\frac{2.51}{N_{R e} \sqrt{f}}\right) \] \( \checkmark \) Find the friction factor \( f \) for \( N_{R e}=6.5 \times 104 \) and \( \varepsilon / D=0.000 \)
Added by Mohamed A.
Close
Step 1
We can do this by using the `numpy` library for mathematical operations and the `math` library for the square root and natural logarithm functions. ```python import numpy as np import math def colebrook(f, N_Re, epsilon_D): return 1/math.sqrt(f) + 0.86 * Show more…
Show all steps
Your feedback will help us improve your experience
David Nguyen and 58 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The Haaland formula for the friction factor is $$f=\frac{0.3086}{\left\{\log \left[6.9 / \mathrm{Rc}+(\varepsilon / 3.7 D)^{1.11}\right]\right\}^{2}}$$ Compare this equation for $f$ for $\varepsilon / D=0.00001,0.0001,0.001$ and 0.01 and Reynolds numbers of $10^{4}, 10^{5}, 10^{6},$ and $10^{7}$ with the Moody chart and decide whether it is an acceptable replacement for the Colebrook formula.
The value of friction force $f$ is (A) $\frac{M g}{2}$ (B) $\frac{M g}{2+\sqrt{3}}$ (C) $\frac{M g}{2(2+\sqrt{3})}$ (D) $\frac{M g}{\sqrt{3}}$
The Swamee and Jain formula for the friction factor is $$f=\frac{0.25}{\left[\log \left(\varepsilon / 3.7 D+5.74 / \mathrm{Re}^{0.9}\right)\right]^{2}}$$ Compare this equation for $\varepsilon / D=0.00001,0.0001,0.001,$ and 0.01 and Reynolds numbers of $10^{4}, 10^{5}, 10^{6},$ and $10^{7}$ with the Moody chart and decide whether it is an acceptable replacement for the Colebrook formula.
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD