Flow of a Non Viscous Fluid Through this Nozzle

[rekordido11]

Homework Statement

Determine the second layer's thickness

Relevant Equations

A1V1=A2V2
V2/V1=(R1ˇ2)/(R2ˇ2)

My first post here!
I have calculated everything i need, except the thickness of the second layer dZ*, therefore i can't solve V3/V2=(R2ˇ2)/(R3ˇ2)
Trying for days now, i would appreciate any help.

 

[Chestermiller]

The problem statement doesn't make a whole lot of sense to me. I guess they expect you to express the result algebraically in terms of $\Delta z^*$.

 

[haruspex]

The problem statement doesn't make a whole lot of sense to me. I guess they expect you to express the result algebraically in terms of $\Delta z^*$.

The way I read it, we are to find R1:R2, and hence v1:v2, in terms of L and Δz.
@rekordido11, think about the ratios between the complete cone and the cone from A2 to the point in respect of lengths and base radii.

 

[rekordido11]

Thank you Haruspex! I'm thinking..
I forgot to mention that i have given values for L=0.1m and Δz = 0.201m and R1=0.01m
Is R1/R2 = R2/R3 ?

 

[haruspex]

Is R1/R2 = R2/R3 ?

No.
Don't worry about R3 yet. You already figured out that to answer the first part you need the ratio of the two areas, A1:A2.
Look at the diagram showing those areas within the whole cone. Think about similar triangles. What equation can you write relating R1, R2, L and Δz?

 

[rekordido11]

No.
Don't worry about R3 yet. You already figured out that to answer the first part you need the ratio of the two areas, A1:A2.
Look at the diagram showing those areas within the whole cone. Think about similar triangles. What equation can you write relating R1, R2, L and Δz?

R1/R2 = L/(L-dZ)
therefore R2/R3 = (L-dZ)/(L-dZ-dZ*)?

 

[haruspex]

R1/R2 = L/(L-dZ)
therefore R2/R3 = (L-dZ)/(L-dZ-dZ*)?

Right, but you are asked for the velocity ratio.
How will you find Δz*?

 

[rekordido11]

Δz* = L-Δz-(the length of the cone with R3)

V2/V3 = (L-Δz)/(the length of the cone with R3)
Am i right?

 

[haruspex]

Δz* = L-Δz-(the length of the cone with R3)

True, so can you find the length of the cone with R3?.

V2/V3 = (L-Δz)/(the length of the cone with R3)

No. In your original attempt you had a correct equation involving the velocities.

 

[rekordido11]

i solved the problem successfully with your help!
my professor approved :)
thank you very much sir!