Momentum and continuity equation

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Discussion Overview

The discussion revolves around a fluid dynamics problem involving the momentum and continuity equations, as well as Bernoulli's equation. Participants are attempting to solve a specific question related to fluid flow through a cone and nozzle, focusing on the application of these equations to determine velocities and forces.

Discussion Character

  • Homework-related
  • Technical explanation
  • Exploratory

Main Points Raised

  • One participant indicates difficulty with part a) of the problem but has calculated velocities v1 and v2 using the continuity equation, yielding v1 = 0.764 m/s and v2 = 8.475 m/s.
  • Another participant confirms that the questions are from old exams intended for revision purposes.
  • A hint is provided suggesting the use of three equations: the continuity equation for flow rates, Bernoulli's equation for pressure relationships, and the momentum equation for relating velocities to forces.
  • There is a question raised about whether the problem is from a take-home exam, which is clarified as being from old exam questions.

Areas of Agreement / Disagreement

Participants generally agree on the relevance of the continuity equation and the need to apply multiple equations to solve the problem. However, there is no consensus on the next steps or the correct application of Bernoulli's equation, as one participant expresses uncertainty about how to proceed.

Contextual Notes

Participants have not fully resolved the mathematical steps required to apply Bernoulli's equation or the momentum equation in conjunction with the continuity equation. There may be assumptions regarding the flow conditions and the definitions of variables that are not explicitly stated.

andyb1990
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Homework Statement



Follow the link to see the question,

http://img507.imageshack.us/img507/2246/fluidquestion.png

Homework Equations





The Attempt at a Solution



currently I can't do part a) but from using part a) I can obtain the forces acting on the cone by using the first part of the equation (ρQ^2/2*A2) and then the force acting on the nozzle by using all of the equation,

for part a) I currently have used the continuity equation to work out what v1 and v2

v1= 0.764 m/s and v2= 8.475 m/s

then I am stuck as what to do with bernoulli's equation if that is the correct next step?
 
Last edited by a moderator:
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andyb1990 said:

Homework Statement



Follow the link to see the question,

http://img507.imageshack.us/img507/2246/fluidquestion.png

Homework Equations





The Attempt at a Solution



currently I can't do part a) but from using part a) I can obtain the forces acting on the cone by using the first part of the equation (ρQ^2/2*A2) and then the force acting on the nozzle by using all of the equation,

for part a) I currently have used the continuity equation to work out what v1 and v2

v1= 0.764 m/s and v2= 8.475 m/s

then I am stuck as what to do with bernoulli's equation if that is the correct next step?

Is this question from a take-home exam?
 
Last edited by a moderator:
no, They are old exam questions to help us revise.
 
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.
 

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