Bernoulli equation gives negative denominator for expanding pipe flow

[levi415]

I'm having problems with what seems like a simple Bernoulli exercise where I can plug in all known variables but not get an answer (using Excel).

If I reduce my system down, it would be exactly like a venturi/pipe flow problem except that flow is in the direction of small pipe to large pipe. P1 and A1 are for small pipe, P2 and A2 are for larger pipe.
P1=60psi
A1=.002in^2 (very small orifice)
P2=55psi
A2=.307in^2
density (rho) air at 90F/60psi=.367lb/ft^3
Bernoulli's eqn at continuity gives flow rate Q = A2*[((2*deltaP)/rho)/(1-(A2/A1)^2)]^0.5

When I plug in the numbers as shown, I get a number error in Excel because the 1-(A2/A1)^2 in the denominator ends up negative.

Any ideas where I might have gone wrong? Thanks very much.

 

[boneh3ad]

Why not just start from the actual Bernoulli equation? You can derive the equation you just cited and determine that your denominator is flipped. It should be
$$\left(\frac{A_2}{A_1}\right)^2 - 1$$

 

[levi415]

Thanks, boneh3ad. I actually did derive the above equation from the original where
P1+0.5*rho*v1^2 = P2+0.5*rho*v2^2. Since A1v1 = A2v2, I solved for v2 and substituted back into the original.
I think my error was... as I was ignoring the sign of my deltaP, I was subtracting from the wrong side of the equation, i.e., I should have been subtracting system 1 variables from system 2 variables. Anyway, I came up with an answer for v2 (instead of finding Q). V is what I want anyway.
What confuses me is... where do the time units come into the equation? How do rho, area, and pressure give me a distance/time unit?

 

[boneh3ad]

The SI unit of pressure, the pascal has units
$$\frac{kg\;m}{s^2\;m^2}$$