The velocity V with which a shell can be fired from a gun barrel depends upon...

 

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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. 1. By using the Buckingham II Theorem and Sequential Elimination, derive the non- dimensional groups of the function. a. State the SI units and the dimensions of each of the five physical variables: V, c, E, m, p, and D. [6/25] b. Use Buckingham II Theorem and Sequential Elimination to find how many independent non-dimensional groups can be formed from the physical quantities in a. [2/25] c. Use the method of sequential elimination of dimensions, derive a non- dimensional form for the following: с = 1 (₁ f E PD¹ mc² m 5 [12/25] 2. In a laboratory test, a shell-like projectile of diameter 10 mm and mass 0.05 kg is fired at a speed of 500 m/s through a heavy gas with a density of 2 kg/m³ and a sound speed of 100 m/s. The explosive energy required is 10 kJ. Calculate the shell speed, shell mass and explosive energy for a geometrically similar shell of 100 mm diameter fired into air with a density of 1.2 kg/m³ and sound [5/25] speed 340 m/s assuming conditions of dynamic similarity. 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. 1. By using the Buckingham II Theorem and Sequential Elimination, derive the non- dimensional groups of the function. a. State the SI units and the dimensions of each of the five physical variables: V, c, E, m, p, and D. [6/25] b. Use Buckingham II Theorem and Sequential Elimination to find how many independent non-dimensional groups can be formed from the physical quantities in a. [2/25] c. Use the method of sequential elimination of dimensions, derive a non- dimensional form for the following: с = 1 (₁ f E PD¹ mc² m 5 [12/25] 2. In a laboratory test, a shell-like projectile of diameter 10 mm and mass 0.05 kg is fired at a speed of 500 m/s through a heavy gas with a density of 2 kg/m³ and a sound speed of 100 m/s. The explosive energy required is 10 kJ. Calculate the shell speed, shell mass and explosive energy for a geometrically similar shell of 100 mm diameter fired into air with a density of 1.2 kg/m³ and sound [5/25] speed 340 m/s assuming conditions of dynamic similarity.

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D 9 Velocity V spead of air c energy E Mass m density P Diameter D b Total no ... View the full answer