Friction factor in drill pipe

Input(s)

$\mu_{\mathrm{s}}$: Static Viscosity $(\mathrm{cP})$

$\sigma$: Normal Stess at Contact (psi)

$\mathrm{k}$: Exponential Constant (dimensionless)

$\mathrm{t}$: Average Contact Time (s)

$\mathrm{V}_{\mathrm{t}}$: Trip Speed $(\mathrm{ft} / \mathrm{s})$

$\omega$: Angular Speed $(\mathrm{ft} / \mathrm{s})$

Output(s)

$\mu$: Constant (dimensionless)

Formula(s)

$$ \mu=\frac{\mu_{\mathrm{s}}}{1+\left(\frac{\mu_{\mathrm{s}} * \sigma *\left(\left(\mathrm{~V}_{\mathrm{t}}^{2}+\omega^{2}\right)^{0.5}\right)}{\mathrm{k} * \mathrm{t}}\right)} $$

Reference(s)

Samuel. E Robello. 501 Solved Problems and Calculations for Drilling Operations. Sigma Quadrant. 2015. Houston, Texas, Page: 375.