Wellbore pressure loss due to friction during hydraulic fracturing (laminar flow)

Input(s)

v: Average Velocity (ft/s)

L: Pipe Length $(\mathrm{ft})$

$d$: Inner Diameter of Pipe (in.)

$\mu_{p}$: Plastic Viscosity $(\mathrm{cP})$

$\tau_{y}$: Yield Point of the Liquid $\left(\mathrm{lb} / 100 \mathrm{ft}^{2}\right)$

Output(s)

$\Delta P_{f}$: Pressure Loss in the wellbore Sourced by Frictions during Hydraulic Fracturing (psi)

Formula(s)

$$ \Delta P_{f}=\frac{\mu_{p} L v}{1500 d^{2}} \cdot \frac{\tau_{y} \cdot L}{225 \cdot d} $$

Reference(s)

Saydam, T., (1967). Principles of Hydraulic Fracturing, ARI Publishing Co., Page: 30.