# Venturi meter pressure difference

1. Jan 4, 2017

### pressurised

1. The problem statement, all variables and given/known data

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

3. The attempt at a solution

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

2. Jan 4, 2017

### TSny

Looks like you made an error in the rearranging. I'm not sure, but it appears that you assumed that $\sqrt{U_2^2 - U_1^2} = U_2 - U_1$

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

3. Jan 5, 2017

### pressurised

Oh I see, if I use A1U1=A2U2 And rearrange for U2, and use d2/D2 for the area ratio?

4. Jan 5, 2017

### TSny

Yes. But you might want to rearrange for U1. Depends on how you are doing the algebra to get to the result.

5. Jan 5, 2017

### pressurised

Thank you! I got it now! :)