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

## Input(s)

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

L: Pipe Length (ft)

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

\(d_{1}\) : Outer Diameter of the Inner 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 due to Frictions during Hydraulic Fracturing (psi)

## Formula(s)

\[
\Delta P_{f}=\frac{\mu_{p} L v}{1000\left(d_{0}-d_{i}\right)^{2}}+\frac{\tau_{y} \cdot L}{200 \cdot\left(d_{0}-d_{i}\right)}
\]

## Reference(s)

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