Need help with fluid mechanics question

[Syn91]

A liquid atomizer has the configuration shown in Figure Q5(http://img822.imageshack.us/img822/8543/figure5.png [Broken]). The liquid is accelerated through the nozzle and impinges on a cone attached to the nozzle by a thin rod. The nozzle is circular in cross-section and coaxial with the rod and cone. Show that the net hydrodynamic force F to be withstood by the flange bolts is F = (ρ*Q^2 / 2*A2) * (A1/A2 + A2/A1 - 2cosθ) \where ρ is the liquid density, Q the liquid volume flow rate, A1 the upstream area of the nozzle, A2 the nozzle leave area and θ is the half angle of the cone. Assume that external to the nozzle, the liquid pressure is equal to that of its surroundings, that there are no losses and gravitational effects are negligible as in the influence of the thin rod on the flow.

 

[LawrenceC]

Hint:

You have 3 equations to work with.

1. Continuity equation relates velocities to flow Q.
2. Bernoulli's equation relates velocities to pressure.
3. Momentum equation relates velocities to pressure force and bolt force.

Use all three and you will get the posted answer. Let's see an attempt.

 

[Syn91]

hi, i did attempt it and where I'm supposed to get -2cosθ, i get -2 only... any advice?

 

[LawrenceC]

You have to show your work here to get help. We will not do the problem for you as it violates the rules of this forum.