Question

A large vessel fitted with a nozzle contains air at a pressure of 2900kn/m² and temperature of 313k .if the pressure at the outlet of the nozzle is 2100kN/m find the velocity and Mach number of air fliwing at the outlet of the nozzle.

Answer 1

To find the velocity and Mach number at the outlet of the nozzle, we can use Bernoulli's equation. The velocity at the outlet of the nozzle is 40kN/m² and the Mach number is 0.117.

Step-by-step explanation:

The correct answer is option C.

To find the velocity at the outlet of the nozzle, we can use the Bernoulli's equation:

P1 + 1/2 ρ V12 = P2 + 1/2 ρ V22

where:

• P1 and P2 are the initial and final pressures respectively
• ρ is the density of the air
• V1 and V2 are the initial and final velocities respectively

Plugging in the given values:

2900kN/m² + 1/2 * ρ * V12 = 2100kN/m² + 1/2 * ρ * V22

Since the temperature is constant, we can assume that the density remains constant as well.

Simplifying the equation gives:

V22 = 2 * (2900kN/m² - 2100kN/m²) = 1600kN/m²

Taking the square root of both sides:

V2 = 40kN/m²

To find the Mach number, we can use the equation:

Mach number = V2 / speed of sound

where the speed of sound at a temperature of 313K is approximately 343m/s.

Plugging in the values, we get:

Mach number = 40kN/m² / 343m/s = 0.117