Interpol Is Late to a
Mind-Blowing Math Hack

Just The Facts

DOFPro Team

Properties of Saturated Steam: Temperature Table

Linear Interpolation

Properties of Saturated Steam: Temperature Table

\[\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}\]

\[y=\frac{y_2-y_1}{x_2-x_1}({x-x_1})+y_1\]

\[\hat{V}=\frac{\hat{V}_2-\hat{V}_1}{T_2-T_1}({T-T_1})+\hat{V}_1\]

\[\hat{V}=\frac{106.3-120.8}{10-8}({9-8})+120.8=113.55\]

Double Linear Interpolation

What if you’re between values in two dimensions

\(T=125\ \mathrm{^\circ C}\)

\(P=0.3\ \mathrm{bar}\)

\(\hat{V}=?\)

Double Linear Interpolation

• Called double interpolation
• Have to do three

The Takeaways

1. Linear interpolation is often used in tables.
2. Remember \(slope = slope\) to write formula.
3. A one-dimensional table requires one interpolation.
4. A two-dimensional table requires double interpolation, which is really three interpolations.

Thanks for watching!
The Full Story companion video is in the link in the upper left. The next video in the series is in the upper right. To learn more about Chemical and Thermal Processes, visit the website linked in the description to find previous and following videos in this series.

The DOFPro Team