Wednesday, November 28, 2012

OLD FAITHFUL


By Rachel Walsh


Old Faithful is a geyser in Yellowstone National Park that is powered by an instrusive pluton that is believed to be at a depth of 2.4 km to 4.8 km below the surface. The water is heated, and pumped through a plumbing system up through many geysers, one of which is old faithful. The height the water can reach is up to 56m. The duration of each eruption is 1.5 to 5 min. and the volume of water can reach up to 32 m3 . I am going to investigate the rate, velocity of water at the hole and the possible pressure by the pluton.

Assumptions:
-                    the plumbing is one vertical pipe of equal diameter through all 3.6 km (average) of the earth to the pluton.
-                    The eruption is at a constant rate.
-                    The change of temperature is irrelevant
-                    The pressure at the opening of the hole is atmospheric

Radius of opening: 0.2m
Possible viscosity of brine:1.3 x 10-3 Pa *s (Francke et al)
Density of brine: 1090 kg/ m3

Rate:
            Q= v/t  to 32 m3 / 300s = 0.11 m3/s


Velocity of water:
            pgh = ½ pvto (9.8 m/s)(56m) = ½ v2
                       
            v = 23.4 m/s

Change in pressure from pluton to surface:

            Q = pR4(deltaP)/8hL √†   0.11 m3/s = p(0.2m)4(deltaP)/8(1.3x10-3 Pa*s)(3600m)

            deltaP = 1100 Pa

Sources:
 Francke, Henning. "Density and Viscosity of Brine: An Overview from a Process Engineers Perspective." Sci Verse. Cheme Der Erde - Geochemistry, n.d. Web.

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