Venturi meter pressure difference

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Homework Help Overview

The discussion revolves around the application of Bernoulli's equation and the principles of fluid dynamics, specifically in the context of a Venturi meter and the relationship between pressure difference and fluid velocities. The original poster attempts to derive expressions related to pressure difference and flow rates, while addressing the challenge of eliminating certain variables.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the rearrangement of Bernoulli's equation to express pressure difference and flow rates. Questions arise regarding the assumptions made in the algebraic manipulations, particularly concerning the relationship between velocities and areas. There is also a discussion on how to express one area in terms of another using the diameters of the flow sections.

Discussion Status

Participants are actively engaging with the problem, providing feedback on each other's reasoning and suggesting alternative approaches to express variables. There is a collaborative effort to clarify misunderstandings and refine the algebraic expressions involved.

Contextual Notes

There is an ongoing examination of assumptions related to fluid flow and area ratios, as well as the implications of these assumptions on the derived equations. The discussion reflects a focus on ensuring the accuracy of the mathematical relationships used in the problem.

pressurised
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Homework Statement


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Homework Equations


p=ρgh
Q=A1U1=A2U2
Bernoulli:
p1+½ρU12+ρgz1=p2+½ρU22+ρgz2

The Attempt at a Solution


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So I got that the pressure difference is gh(ρm-ρ). So I rearranged Bernoulli for p1-p2 to get (assuming the potential is the same I eliminated it),

p1-p2=½ρU22-½ρU12
I carried on rearranging to get:
√(2gh(ρm-ρ))/ρ = Q/A2-Q/A1

I am unsure how to eliminate A1 so I can proceed with the question
 
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pressurised said:
p1-p2=½ρU22-½ρU12
I carried on rearranging to get:
√(2gh(ρm-ρ))/ρ = Q/A2-Q/A1
Looks like you made an error in the rearranging. I'm not sure, but it appears that you assumed that ##\sqrt{U_2^2 - U_1^2} = U_2 - U_1##

I am unsure how to eliminate A1 so I can proceed with the question
How can you express A1 in terms of A2 and the diameters D1 and D2?
 
TSny said:
Looks like you made an error in the rearranging. I'm not sure, but it appears that you assumed that ##\sqrt{U_2^2 - U_1^2} = U_2 - U_1##

Thank you it seems I did.

How can you express A1 in terms of A2 and the diameters D1 and D2?

Oh I see, if I use A1U1=A2U2 And rearrange for U2, and use d2/D2 for the area ratio?
 
pressurised said:
Oh I see, if I use A1U1=A2U2 And rearrange for U2, and use d2/D2 for the area ratio?
Yes. But you might want to rearrange for U1. Depends on how you are doing the algebra to get to the result.
 
TSny said:
Yes. But you might want to rearrange for U1. Depends on how you are doing the algebra to get to the result.

Thank you! I got it now! :)
 

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