At any time, approximately 20 volcanoes are actively erupting on the Earth, and 50–70 volcanoes erupt each year. Over the past 100 years, an average of 850 people have died each year from volcano eruptions. As scientists and engineers study the mechanics of lava flow, accurately predicting the flow rate (velocity) of the lava is critical to saving lives after an eruption. Jeffrey’s equation captures the relationship between flow rate and viscosity as:

where ρ is the density of the lava, g is gravity, t is the flow thickness, α is the slope, and α is the lava viscosity. Typical values for the viscosity and density of lava are 4.5 x 10³ kg/(m ∙ s) and 2.5 g/cm³, respectively. Find the velocity of the flow in Figure P6.20 in cm/s and mph.

Figure P6.20

Transcribed Image Text:

V = pgt sin(a) 3µ