The velocity V with which a shell can be fired from a gun barrel depends upon the shell diameter D, the shell mass m, the air density P, the speed of sound of the air and the explosive energy of the shell E. After dimensional analysis, one student found that II, = %i H2=%5Ha=% Based above analysis results, answer the following question: In a laboratory test, a shell-like projectile of diameter [Dm] mm and mass [mm] kg is fired at a speed of [Vm] m/s through a heavy gas with a density of [rhom] kg/m? and a sound speed of [Cm] m/s. The explosive energy required is [Em] kJ. Calculate the shell speed for a geometrically similar shell of [Dp] mm diameter fired into air with a density of [rhop] kg/m3 and sound speed [Cp] m/s assuming conditions of dynamic similarity (with 2 decimal places). Variables Variable Min Max Decimal places Dm 7.0 12.0 0 mm 0.03 0.07 2 Vm 400.0 600.0 O rhom 1.0 4.0 0 Cm 90.0 1200 O Em 7.0 12.0 0 Dp 80.0 1300 O rhop 0.98 1.4 2 Cp 300.0 4000 O Formulas Vm*Cp/Cm The velocity V with which a shell can be fired from a gun barrel depends upon the shell diameter D, the shell mass m, the air density p, the speed of sound of the air c and the explosive energy of the shell E. After dimensional analysis, one student found that I1 = ; I12 = mc2 ; I13 = PD's m Based above analysis results, answer the following question: In a laboratory test, a shell-like projectile of diameter [Dm] mm and mass [mm] kg is fired at a speed of [Vm] m/s through a heavy gas with a density of [rhom] kg/m3 and a sound speed of [Cm] m/s. The explosive energy required is [Em] KJ. Calculate the shell mass for a geometrically similar shell of [Dp] mm diameter fired into air with a density of [rhop] kg/m's and sound speed [Cp] m/s assuming conditions of dynamic similarity (with 2 decimal places). Variables Variable Min Max Decimal places Dm 3.0 12.0 0 mm 0.03 0.08 2 Vm 400.0 600.0 0 rhom 1.0 3.0 0 Cm 90.0 120.0 0 Em 90.0 110.0 0 Dp 80.0 110.0 0 rhop 1.0 1.5 Cp 300.0 400.0 0 Formulas rhop*Dp^3*mm/(rhom*Dm^3)