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Maybe they are assuming that the fluid pressure in the pipe is just atmospheric pressure (zero gage), or maybe they just inadvertently left out the pressure force.Vibhor said:
Why is the force on the fluid not equal to the change in momentum per unit time?
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Discussion Overview
The discussion centers on the relationship between the force acting on a fluid in a pipe and the change in momentum per unit time, particularly in the context of fluid dynamics involving a right-angle bend in the pipe. Participants explore the concepts of momentum flow, rate of change of momentum, and the implications of these for understanding forces in fluid systems.
Discussion Character
- Technical explanation
- Debate/contested
- Mathematical reasoning
Main Points Raised
- One participant questions why the force on the fluid is not equal to the change in momentum per unit time, suggesting confusion between flow of momentum and change in momentum.
- Another participant asserts that force is the rate of change of momentum and prompts others to consider the units involved in their calculations.
- Some participants express that while the calculations may be dimensionally correct, they do not logically equate to the rate of change of momentum.
- There is a discussion about how to calculate the rate of change of momentum, with one participant providing a method involving the time taken for fluid to pass through a corner.
- One participant introduces the concept of a control volume to analyze the flow of momentum into and out of a system, providing detailed calculations for momentum changes.
- Concerns are raised about the assumptions made in the calculations, such as the constancy of velocity and density, and the implications of varying these parameters.
- Another participant discusses the potential effects of compressibility and laminar flow on the analysis.
- There are multiple examples provided to illustrate the forces on a bend due to mass flow and flow velocity, with calculations for specific scenarios.
- One participant questions whether pressure should be included in the force calculations, indicating a potential oversight in the analysis.
Areas of Agreement / Disagreement
Participants express differing views on the relationship between momentum flow and force, with no consensus reached on whether the change in momentum flow rate equates to the rate of change of momentum. The discussion remains unresolved regarding the implications of varying fluid properties and the assumptions made in the calculations.
Contextual Notes
Limitations include assumptions about fluid incompressibility, constant density and velocity, and the nature of the flow (laminar vs. turbulent). The discussion also highlights the complexity of analyzing fluid behavior in bends and the need for careful consideration of forces acting on the fluid.
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