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andyb1990
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Would you subtract the square root from the right hand side to get A2 on its own, then group like terms?
Bernoulli's Equation- on a jet nozzle
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Discussion Overview
The discussion revolves around deriving equations related to the flow of a liquid jet from a nozzle, specifically focusing on the jet speed at the nozzle exit, the jet speed at a vertical distance below the nozzle, and the cross-sectional area of the jet at that distance. The context includes theoretical aspects of fluid dynamics, particularly applying Bernoulli's equation and the continuity equation.
Discussion Character
- Homework-related
- Mathematical reasoning
- Technical explanation
- Debate/contested
Main Points Raised
- Participants discuss the application of the continuity equation to derive the jet speed at the nozzle exit and at a distance below the nozzle.
- Some participants propose that the stagnation pressure at the nozzle exit is crucial for calculating the jet speed.
- There are differing views on how to express the equations, particularly regarding the correct formulation of the Bernoulli equation and the relationship between pressure, velocity, and height.
- Participants challenge each other's algebraic manipulations and the implications of their derived equations, particularly concerning the conservation of mass.
- There is a suggestion that the area of the jet at a distance below the nozzle should be derived from the mass flow rate equations, but confusion arises regarding the correct algebraic steps to take.
Areas of Agreement / Disagreement
Participants do not reach a consensus on the correct derivations and algebraic manipulations. Multiple competing views remain regarding the correct expressions for the jet speed and area, as well as the implications of the conservation of mass.
Contextual Notes
There are unresolved issues regarding the assumptions made in the derivations, particularly concerning the treatment of pressure and the effects of gravity on the jet flow. Participants also express uncertainty about the algebraic steps necessary to arrive at the correct equations.
Who May Find This Useful
This discussion may be useful for students studying fluid dynamics, particularly those working on problems involving Bernoulli's equation and the continuity equation in the context of jet flow from nozzles.
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