The work done during polytropic expansion of gas from state 1 to state 2 is given by: 1 W = - (P₂V₂ - P₁V₁) 1-n A pressurised reservoir connected to a vertical barrel is used to launch projectiles as shown in Figure Q2.1. Assume no leakage around the projectile, no friction and no pressure drop across the valve. The barrel is cylindrical with a diameter, D = 50mm and a length, L = 0.8m. The mass of the projectile, M = 1kg. The volume of the reservoir, V = 2 litres. Atmospheric pressure is 1.01 bar. L M Barrel Valve Figure Q2.1 Reservoir Volume, Vr a) By applying conservation of energy, for an initial reservoir pressure and temperature of 2bar and 20degC and assuming polytropic expansion with n= 1.3, find the exit velocity of the projectile. b) If the valve shuts at the instant the projectile leaves the barrel, what mass of gas is used to launch the projectile? c) Prove that a barrel length of 0.64m results in maximum exit velocity. d) Using this barrel length, what is the maximum height reached by the projectile after it leaves the barrel if drag is neglected?

The work done during polytropic expansion of gas from state 1 to state 2 is given by: 1 W = - (P₂V₂ - P₁V₁) 1-n A pressurised reservoir connected to a vertical barrel is used to launch projectiles as shown in Figure Q2.1. Assume no leakage around the projectile, no friction and no pressure drop across the valve. The barrel is cylindrical with a diameter, D = 50mm and a length, L = 0.8m. The mass of the projectile, M = 1kg. The volume of the reservoir, V = 2 litres. Atmospheric pressure is 1.01 bar. L M Barrel Valve Figure Q2.1 Reservoir Volume, Vr a) By applying conservation of energy, for an initial reservoir pressure and temperature of 2bar and 20degC and assuming polytropic expansion with n= 1.3, find the exit velocity of the projectile. b) If the valve shuts at the instant the projectile leaves the barrel, what mass of gas is used to launch the projectile? c) Prove that a barrel length of 0.64m results in maximum exit velocity. d) Using this barrel length, what is the maximum height reached by the projectile after it leaves the barrel if drag is neglected?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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