Question

Extra Credit Problem (10 pts) If the principle reservoir feeding the mountain with liquid magma is a spherical volume having a diameter of roughly 1 km and is located 7 km below and 2 km to the south of the lava dome at the summit of the mountain, estimate the average pressure in atmospheres of the magma inside of the reservoir if the lava level in the lake is steady and assuming that the magma is liquid everywhere from the reservoir to the lava lake at the summit (i.e., that no plug has formed in the main vent. Assume that the density of the liquid magma is the same as that of the solid basalt and neglect any gasification that might occur or temperature variations.

Answer 1

• let the pressure at top of the mountain be atmospheric pressure
• The pressure of reservoir can be found by applying bernoullis equation

Given Data dalkm , hz 7km, L22km E mountain halokm Reservoir Lz2km apply bernoulli's equation between © and ® sig andere acis here, Piz Patmosphen z 1.0, bar P z atmospheric prestire of resemoig 8,2822 density of solid basalt = 3011 kg so, from cil 11.018105+10110?)3011498/2 po m3 Po z 32787.08 bar