# Back-of-the-Envelope Calculations: Rate of Lava Flow

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This page first made public: Oct 28, 2005

#### Summary

*Question*

In 1983, an eruption began at Kilauea Volcano in Hawaii that has proved to be the largest and longest-lived eruption since records began in 1823. Lava has poured out of the volcano at an average rate of about 160 million m^{3} per year. To put those flow rates into perspective, let's suppose that the volcano was erupting directly into your classroom. At these flow rates, how long would it take to fill your classroom with lava?

## Assessment

*Answer*

About one minute! If your classroom is about 10 m x 10 m x 3 m (30' x 30' x 9'), your classroom would hold about 300 m^{3} of lava. 160 million m^{3} per year is about 5 m^{3} per second (there are 31,536,000 seconds in a year). If you filled your classroom with lava at the rate of 5 m^{3} per second, it would take only 60 seconds to fill your classroom! Imagine having a hose big enough to fill your classroom with water that fast!

## References and Resources

This SERC page describes the use of Back of the Envelope Calculations

A View from the Back of the Envelope (more info) : This site has a good number of easy simulations and visualizations of back of the envelope calculations.

The Back of the Envelope : This page outlines one of the essays in the book "Programming Pearls" (ISBN 0-201-65788-0). The book is written for computer science faculty and students, but this portion speaks very well to back of the envelope calculations in general.

## Controlled Vocabulary Terms

**Subject**: Geoscience:Geology:Igneous and Metamorphic Petrology:Volcanology, Environmental Science:Natural Hazards:Volcanism

**Resource Type**: Activities:Classroom Activity:Short Activity

**Special Interest**: Quantitative, Hazards

**Grade Level**: High School (9-12), College Lower (13-14), College Upper (15-16)

**Quantitative Skills**: Estimation, Graphs

**Ready for Use**: Ready to Use

**Theme**: Teach the Earth:Course Topics:Environmental Science, Teach the Earth:Teaching Topics:Volcanoes, Teach the Earth:Incorporating Societal Issues:Hazards, Teach the Earth:Course Topics:Petrology

**Topics**: Solid Earth