Question

Consider a steady isentropic airflow through a convergent channel with an inletto-exit cross section area ratio of 2. If the inlet flow Mach number is 0.2, what is the Mach number at the exit? If the inlet flow Mach number is 2.5, what is the Mach number at the exit?

Answer 1

Answer:

for m1=0.2

M2=0.4

for m1=2.5

M2=5

1=  channel input

2.channel output

Explanation:

Hello!

To solve this problem follow the steps below!

1.As it is an isentropic system, it means that the temperature of the fluid remains constant, so the volumetric flow is the same, remember that this is calculated by calculating the product between the velocity and the area.

V1A1=V2A2

1=  channel input

2.channel output

We can divide both sides of the equation by the speed of sound(V)

$\frac{V1}{V}A1= \frac{V2}{V}A2$

2. The mach number is defined as the ratio between the speed of a fluid and the speed of sound,

we rearrange the equation

M1A1=M2A2

$\frac{M1A1}{A2} =M2$

3.Now considering that the channel is convergent and that the ratio between the areas is 2, we have the following equation (A1 / A2 = 2)

M1(2)=M2

4.Finally we solve for the number of mach indicated (0.2 and 2.5)

for m1=0.2

0.2(2)=M2=0.4

for m1=2.5

2.5(2)=M2=5