# 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.