Air enters the diffuser of a jet engine operating at steady state at 18 kpa, 216 k and a velocity of 265 m/s, all data corresponding to high-altitude flight. the air flows adiabatically through the diffuser and achieves a temperature of 250 k at the diffuser exit. using the ideal gas model for air, determine the velocity of the air at the diffuser exit,

45.44m/s

Explanation:

To solve this problem it is necessary to go back to the concepts related to the first law of thermodynamics,

in which it deepens on the conservation of the Energy.

The first law of Thermodynamics is given by the equation:

Where,

Heat transfer

Work

Flow mass

Velocity

Specific Enthalpy

Gravity

Height

From this equation we have that there is not Heat transfer, Work and changes in Height. Then,

Then our equation would be,

Solving for

From the tables of ideal gas (air) at 216K we have,

From the tables at 250K, we have that

The velocity was previously given, then

Replacing in the equation:

Therefore the velocity of the air at the diffuser exit is 45.44m/s

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s

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