Flow of a Non Viscous Fluid Through this Nozzle

AI Thread Summary
The discussion revolves around calculating the thickness of the second layer (dZ*) in a fluid flow problem through a nozzle. The original poster struggled to express the velocity ratios V3/V2 and R1:R2 algebraically in terms of Δz*. Through collaborative input, they were guided to focus on the ratios of areas and the relationships between the cone's dimensions. Ultimately, they successfully solved the problem with assistance, receiving approval from their professor. The thread highlights the importance of understanding geometric relationships in fluid dynamics.
rekordido11
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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.
 

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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^*##.
 
Chestermiller said:
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.
 
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 ?
 
Last edited:
rekordido11 said:
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?
 
haruspex said:
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*)?
 
rekordido11 said:
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*?
 
Δz* = L-Δz-(the length of the cone with R3)

V2/V3 = (L-Δz)/(the length of the cone with R3)
Am i right?
 
rekordido11 said:
Δz* = L-Δz-(the length of the cone with R3)
True, so can you find the length of the cone with R3?.
rekordido11 said:
V2/V3 = (L-Δz)/(the length of the cone with R3)
No. In your original attempt you had a correct equation involving the velocities.
 
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i solved the problem successfully with your help!
my professor approved :)
thank you very much sir!
 

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