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.