How Do You Calculate Force on an Orifice Plate in Fluid Mechanics?

[Jsp83]

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I am having difficultly with a problem in my fluid mechanics course and I'm hoping someone could help me out.

Here is a screenshot of the question I'm stuck on:

So far I have been using Bernoulli equation to find the pressure in the pipe, assuming atmospheric pressure at the point where the stream is released. This gives p₁ + 0.5ρv₁² = p_atmos + 0.5ρv₂²
Where v₂ = v₁A₁/A₂

I have then been using the Reynolds transport theorem to find the force on the plate:
m(v₂-v₁) + p₁A₁ = P_atmosA₂ + F_x
Where m is the mass flow rate, m = ρAv₁
and F_x is the force I am solving for.

Can anyone find anything wrong with this method, as I have checked my calculations many times but constantly get the wrong answer.

Thanks in advance

 

[Chestermiller]

The signs on some of the terms in the momentum balance are incorrect.

m(v2-v1)= (sum of forces in +x direction) - (sum of forces in -x direction)

Chet

 

[Jsp83]

Ah, so obvious now... thanks for your help