Air is flowing through a rocket nozzle.Inside the rocket the air has a density of 5.25 kg/m³ and a speed of 1.20 m/s.The interior diameter of the rocket is 15.0 cm.At the nozzle exit,the diameter is 2.50 cm and the density is 1.29 kg/m³.What is the speed of the air when it leaves the nozzle? A)123 m/s B)176 m/s C)88.0 m/s D)45.7 m/s E)29.3 m/s

Question

Quizplus · Accepted Answer

This problem can be solved using the principle of conservation of mass and conservation of momentum. The mass flow rate (m dot) remains constant throughout the nozzle.

m dot = density x area x velocity

At the rocket interior: 
m dot = 5.25 kg/m^3 x pi x (0.15 m/2)^2 x 1.20 m/s = 0.221 kg/s

At the nozzle exit: 
m dot = 1.29 kg/m^3 x pi x (0.025 m/2)^2 x v

Setting the two mass flow rates equal to each other: 
5.25 kg/m^3 x pi x (0.15 m/2)^2 x 1.20 m/s = 1.29 kg/m^3 x pi x (0.025 m/2)^2 x v

Solving for v, we get: 
v = 176 m/s

Therefore, the answer is B.

Air Is Flowing Through a Rocket Nozzle