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 is a problem involving the principle of conservation of mass and conservation of energy. The equation we need to use is:

ρ1A1v1 = ρ2A2v2      (conservation of mass)

where ρ is density, A is cross-sectional area, and v is velocity. We also need to use the equation for conservation of energy:

(1/2)ρ1v1^2 + P1/ρ1 = (1/2)ρ2v2^2 + P2/ρ2

where P is pressure.

Substituting the given values, we get:

(5.25 kg/m3)(π/4)(0.15 m)^2(1.20 m/s) = (1.29 kg/m3)(π/4)(0.025 m)^2v2

Solving for v2, we get:

v2 = 176 m/s

Therefore, the answer is B.

Air Is Flowing Through a Rocket Nozzle