Pyroclastic Rocks                                                                                                       GLY431/531

Homework Problem

Magma Flow in Conduits

        A basaltic volcano with a 5 m diameter conduit erupts magma with a viscosity (m) of 10³ poises and a density of 2,800 kg/m³.  Assume that isothermal Poiseuille flow occurs and use the equations shown below to answer the following questions.   Be sure that your units are consistent!

EQ1.       V_aver=(R²/8m)dp/dx

EQ 2.        R_e= rRV/m

        A.    What would be the mean velocity and volume discharge for a pressure drop of 10^-2 bar per km?

        B.    What would be the mean velocity and volume discharge for a pressure drop of 1 bar per km?

        C.    What is the Reynolds number for the above two cases?

        D.    Is the assumption of laminar flow valid?

        E.     How would these two cases compare with effusion at Paricutin, Mexico?

                It had a mass discharge 5 m³/sec in 1945.