2. During the 2005 eruption of Sierra Negra volcano in the Galapagos (I was ther

Question

2. During the 2005 eruption of Sierra Negra volcano in the Galapagos (I was there!), the lava fountain rose 450 m above the vent. Because most of the lava ended up ponding in the caldera, we could establish the average flux of lava (volume with time), which was 100 m3/sec. a) Neglecting air resistance, calculate the velocity of the lava as it was exiting the vent! (Hint: this is the projectile problem in physics, by which: height = velocity2/2 x gravity The velocity of lava exiting the vent at Sierra Negra was _________________________ b) Use this average velocity and the flux (given above) to calculate the diameter of the vent. Hint: this is calculated the same as a stream discharge problem… stream area x velocity = discharge or flux. Do it backwards, you know flux and velocity, assume a circular vent. Remember the formula for a circle? If not…Google. The diameter of the Sierra Negra vent was ____________________________ c) The style of flow of fluids (laminar or turbulent) is controlled by the dimensionless Reynolds number (Re). If Re > 2300, then flow is turbulent: Re (pipe flow) = (vent diameter * density * velocity)/ viscosity Basaltic magmas typically have viscosities of 300 Pa s (note: 1 Pa s = kg m-1 s-1). (Hint…if you do the math correctly, all the units should cancel since Re# is dimensionless!) So, is the magma flow turbulent or laminar in the Sierra Negra conduit? The Re for the Sierra Negra magma was ____________ so the flow was_________________

Explanation / Answer

Ans : Given flux rate( f)=100 m3/sec ;heigth h= 450 m ; take v be the velocity of flow.

a) now h= v^2/(2*g) So, v =sqrt( 2*g*h) =93.9 m/sec.

b) if r be its radius then pi*r^2 *v =flux rate(f) ; so r=sqrt(f/(pi * v)) =0.58 m

c)Re= (r * rho *v)/viscosity = (0.58*93.9)/300 =0.182

Henc magma flow was laminar.

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