# Fluid Mechanics- Venturi Meter Problem

1. Dec 4, 2007

### proponents

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

Air flows through a venturimeter as shown below (rudimentary sketch of a typical venturi meter pictured). Neglecting frictional effects, obtain an expression for the volume flow rate in terms of pressures P1, Pthroat and areas A1, At at the inlet and the throat respectively. Assume density is constant.

2. Relevant equations

I don't know how to include symbols, so I'll do my best.

Q=Mass flow/ ro(density)

mass flow for venturi meter= [(CAt)/(sqrt(1-beta^4)]*sqrt(2*ro*(P1-P2))

beta=Dt/D1

3. The attempt at a solution

I don't think I have enough information. I end up with this equation:

Q= M/ro= [(CAt)/(ro*sqrt(1-beta^4)]*sqrt(2*ro*(P1-P2))

This does not get me Q in terms of P1, P2, A1, and A2. I can assume 0.99 for C assuming Re>2x10^5.

I can change beta into terms of area by: beta=Dt/D1= sqrt(At/A1)

Now I have Q in terms of P1, Pt, A1, At, and ro. Am I supposed to assume a value for density? It seems that the mention of density being constant is supposed to eliminate it. It seems odd that it is the thorn in my spine and it was specifically mentioned in the problem. Also, how can it be constant? We are dealing with air, so the change in pressure would change the density unless the temperature changed proportionately, no? If anyone can tell me what I am doing wrong or if I am missing something it would be greatly appreciated. Thanks!