## Calculating Viscosity (Grades 9-12)

Students have an intuitive understanding of viscosity. This exercise is designed to introduce a simple method used to estimate the viscosity of lava. Information for teachers is presented below. Click here for the handout for students.

Jefferys (1925) derived a formula to calculate the viscosity of a fluid based on its physical properties and flow characteristics. The formula is:

where **V** is the mean velocity of the flow, **g** is the acceleration of gravity, **A** is the angle of the slope, **h** is the depth of the flowing liquid, **p** is the specific gravity of the liquid, and **n** is the coefficient of viscosity.

Geologists realized they could apply this equation to flowing lava to estimate its viscosity. Macdonald (1954) calculated the viscosity of lava during Mauna Loa eruptions he observed in 1940, 1942, 1949, and 1950. In the field he measured the angle of the slope, depth of the lava, and velocity of the flow. Angle of the slope can be measured from a compass or calculated from a topographic map. The depth of the lava channel is used as an approximation of the depth of the lava. Velocity is calculated by throwing a stick on the surface of a flow and measuring the amount of time it travels a premeasured distance. The acceleration of gravity and the specific gravity of the liquid are constants. The acceleration of gravity is 9.8 m/sec2. The specific gravity of cool, basaltic rock is 2.65 gm/cm3; therefore, the specific gravity of hot, basaltic lava must be less than this value. Macdonald used a value of 2 gm/cm3.

The table in activity 14.6 provides Macdonald's estimate of velocity of the flow, depth of the flowing lava, and angle of the slope. Students must use the estimates and the equation to calculate the viscosity. The units for viscosity used by Macdonald are poises. A poise is 1gm/cm s. Therefore, to make the calculations, all measurements must be converted from meters to centimeters. When complete the table should appear as follows:

Based on their calculations, the students must answer the following questions:

**Which eruptions had the lowest viscosities?**

The 1940 and 1942 eruptions had the lowest viscosities.

**Why are the viscosities low for these eruptions?**

The lava was close to the vent and probably very hot and fluid.

**Which eruptions had the highest viscosities?**

The June 1 and 2, 1950, eruptions had the highest viscosities.

**Why is the viscosity high for these eruptions?**

One is an average value for an entire flow. The other was measured far from the vent. Farther from the vent, the lava is cooler and more viscous.

**In general, do the estimates show that viscosity increases with distance from the vent?**

Yes. Measurements near the vent yielded low viscosity values. Measurements far from the vent yielded high viscosity values.