# Annulus pressure loss due to friction during hydraulic fracturing (turbulence flow)

## Input(s)

\(\rho\): Liquid Density (lb/gal)

v: Average Velocity \((\mathrm{ft} / \mathrm{s})\)

\(f\): Fanning Friction Factor (dimensionless)

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

\(d_{0}\) : Inner Diameter of the Outer Pipe (in.)

\(d_{1}\) : Outer Diameter of the Inner Pipe (in.)

## Output(s)

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

## Formula(s)

\[
\Delta P_{f}=\frac{f \cdot L \cdot \rho \cdot v^{2}}{25.80 \cdot\left(d_{0}-d_{i}\right)}
\]

## Reference(s)

Saydam, T., (1967). Principles of Hydraulic Fracturing, ARI Publishing Co., Page: 31.