Using the volcanic flow model and flow parameters from Problem P6.20, prepare two charts.

(a) On one chart, plot the flow velocity in mph as a function of the slope, varying the slope from 08 to 908.

(b) On the other chart, plot the fl ow velocity in mph as a function of the flow thickness, varying the thickness from 0 to 300 cm.

(c) Discuss and compare the influence of the slope and the thickness on the flow velocity.

Problem 6.20

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

V = pgt sin(a) 3