Pressure loss due to sudden enlargement

Input(s)

$\rho$: Density of Fluid $(\mathrm{g} / \mathrm{cc})$

$v_{1}$: Input Velocity $(\mathrm{m} / \mathrm{s})$

$v_{2}$: Output Velocity $(\mathrm{m} / \mathrm{s})$

Output(s)

$\beta$: Velocity Ratio (dimensionless)

$\boldsymbol{p}_{\mathbf{2}}-\boldsymbol{p}_{\mathbf{1}}$: Pressure Drop $(\mathrm{Pa})$

Formula(s)

$$ \begin{gathered} \beta=\frac{\mathrm{v}_{\mathrm{o}}}{\mathrm{v}_{\mathrm{i}}} \\ \mathrm{p}_{2}-\mathrm{p}_{1}=\rho *\left(\mathrm{v}_{2}^{2}\right) *\left(\left(\frac{1}{\beta}\right)-1\right) \end{gathered} $$

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley \& Sons, Chapter: 7, Page: 210.