Venturi meter pressure difference

[pressurised]

Homework Statement

Homework Equations

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

The Attempt at a Solution

[/B]
So I got that the pressure difference is gh(ρ_m-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(ρ_m-ρ))/ρ = Q/A₂-Q/A₁

I am unsure how to eliminate A₁ so I can proceed with the question

 

[TSny]

p₁-p₂=½ρU₂²-½ρU₁²
I carried on rearranging to get:
√(2gh(ρ_m-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?

 

[pressurised]

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?

 

[TSny]

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.

 

[pressurised]

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! :)