Need help with fluid mechanics question

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Discussion Overview

The discussion revolves around a fluid mechanics problem involving a liquid atomizer, specifically focusing on deriving the net hydrodynamic force that the flange bolts must withstand. The problem includes the application of fluid dynamics principles such as the continuity equation, Bernoulli's equation, and momentum considerations.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents a formula for the net hydrodynamic force F, incorporating variables such as liquid density, volume flow rate, and areas of the nozzle.
  • Another participant suggests using three fundamental equations of fluid mechanics: the continuity equation, Bernoulli's equation, and the momentum equation, to derive the solution.
  • A participant expresses difficulty in obtaining the term -2cosθ in their calculations, instead arriving at -2, and seeks advice on this discrepancy.
  • Another participant emphasizes the importance of showing work for assistance, indicating that direct solutions are not provided in the forum.

Areas of Agreement / Disagreement

Participants generally agree on the need to apply fundamental fluid mechanics equations to solve the problem, but there is a disagreement regarding the specific calculations leading to the term -2cosθ, which remains unresolved.

Contextual Notes

Limitations include potential missing assumptions in the derivation, dependence on the definitions of the variables, and the need for clarity in the application of the equations involved.

Syn91
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A liquid atomizer has the configuration shown in Figure Q5(http://img822.imageshack.us/img822/8543/figure5.png ). 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.
 
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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.
 
hi, i did attempt it and where I'm supposed to get -2cosθ, i get -2 only... any advice?
 
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.
 

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