OLD FAITHFUL

By Rachel Walsh

http://www.youtube.com/watch?v=LWrklFuYnb0

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 pv²  to (9.8 m/s)(56m) = ½ v²

                       

            v = 23.4 m/s

Change in pressure from pluton to surface:

            Q = pR⁴(deltaP)/8hL à   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.