Problem Set: Volcanic Hazards Objective of Exercise: To assess the impact of viscosity on lava flow rates and the potential hazard posed by lava. Magma Viscosity: You are the scientist in charge of monitoring two volcanoes on the island of Bastet. Unfortunately, both volcanoes have begun to erupt, each producing lava flows that are threatening a village situated between the two volcanoes at 450 m elevation. The residents are concerned for their safety and have turned to you for help. They want to know when they will need to evacuate. Here is what you know:

A. The village is 4 km from the volcano Sekhmet which is erupting andesite magma at 950C from a vent at 3000 m elevation. The lava flow is 2.5-m-thick and has a density of 2.3 g/cm3. The viscosity of the magma is 1.3 x 106 poise.

B. The village is 18 km from the volcano Osiris which is erupting alkali basaltic magma at 1200C from a vent at 2900 m elevation. The lava flow is 2.0-m-thick and has a density of 2.50 g/cm3. The viscosity of the magma is 1.4 x 104 poise.

C. The relationship for the velocity V (cm/s), of a lava flow on a slope is given by; V = g d2 (sin ) / 4 where is the magma density (g/cm3), g is the acceleration due to gravity (9.8 m/s2), d is the flow thickness (cm), is the magma viscosity (in poise), and is the slope in degrees.

1) Make sure you convert all units (as needed) into centimeters. For example, gravity is given to you in meters, so you need to convert it to cm. However, the units for viscosity poise are already in centimeters. Convert gravity into cm (not poise into m).

2) Calculate how fast the flow from Sekhmet is advancing (in meters per hour) and record your answer. Show all your work and keep units straight!! (5 pts)

3) Calculate how fast the flow from Osiris is advancing (in meters per hour) and record your answer. Show all your work and keep units straight!! (5 pts)

4) How much time in hours do the villagers have to evacuate their homes before the lava from Sekhmet arrives? Show all the math steps needed for conversion (3 pts)

5) How much time in hours do the villagers have to evacuate their homes before the lava from Osiris arrives? Show all the math steps needed for conversion (3 pts)

6) The lava flow from which volcano will inundate the village first? (1 pt)