Can Momentum Conservation Apply to Pressure Change Rates at a Fixed Point?

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Discussion Overview

The discussion revolves around the application of conservation of momentum to the rate of change of pressure at a fixed point in a fluid system, particularly in the context of measurements taken along a pipe influenced by a pump. Participants explore the relationship between pressure changes and momentum in fluid dynamics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant, Sarah, proposes that the conservation of momentum can be applied to pressure changes at a fixed position, suggesting a relationship between the rates of change of pressure, dP1 and dP2.
  • Another participant, Warren, challenges the applicability of momentum conservation in this context and requests more details about the problem being addressed.
  • Sarah elaborates on the problem, describing measurements of pressure changes at various points in a pipe and suggesting that these changes can be explained through momentum conservation principles.
  • A participant questions whether the cross-sectional area of the pipe changes, implying that this could affect the applicability of Bernoulli's Equation and the behavior of pressure in the fluid.
  • Sarah confirms that the cross-sectional area does change along the pipe and expresses interest in studying the relationship between pressure change rates and pumping power.
  • Another participant supports the relevance of Bernoulli's Equation, indicating its relationship to fluid speed and pressure, and inquires about the measurement methods used.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the applicability of momentum conservation to the scenario described. While some support the idea, others challenge it, leading to an unresolved discussion on the topic.

Contextual Notes

There are limitations regarding the assumptions made about fluid behavior, such as the incompressibility of the fluid and the effects of changing cross-sectional area on pressure dynamics. The discussion also reflects uncertainty about the relationship between pressure changes and momentum in this specific context.

sarahh
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Dear Sir/Madam,

I would like to know if I can apply the conservation of momentum to the rate of change of pressure at a fixed position (for e.g. x=0) as follows:
dP1/dt=-dP2/dt

where dP1 is the pressure changes over a fixed interval of time (del t1) and dP2 is the pressure changes over another fixed interval of time (del t2) at x=0, and del t1 = del t2.

Can I explain the above equation as follows:
at x=0, pressure increases by dP1 in del t1 and this dP1/dt is balanced by an equivalent negative rate of momentum changing force per unit area, -dP2/dt after certain period of time.

Thank you very much for your kind assistance.

Sarah
 
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The conservation of momentum does not apply at all.

Perhaps you should tell us the entire problem you're trying to solve?

- Warren
 
Urgent, Please Help

Thank you for the reply.

Our problem is that we measured the rate of change of pressure of a liquid at different length of a pipe, for example, x=0, x=5cm, ... etc, caused by a pump at x=0-15cm=-15cm and got a result that at x=0, dP1/dt1 = -dP2/dt2, where dP1 is the pressure difference over a fixed interval, del t1, and dP2 is the pressure difference over a fixed interval, del t2,
i.e. -----------
- -
- -
del t1 |3 minutes | del t2
(just like a trapezium without the bottom part), and del t1=del t2. Pumping power is decreasing from t=0 to t=4minutes and pumping power =0 when t>4 minutes.
Is it accurate if we try to explain this observation as follows:
Due to conservation of momentum, the rate of momentum-changing force per unit area, dP1/dt, produced by the pump is balanced by an equivalent negative rate of momentum-changing force per unit area, -dP2/dt produced by the system after 3 minutes at x=0.

Thanks again!

Sarah
 
Last edited:
Does the cross-sectional area of the pipe change? I would think that if you assume the fluid to be relatively incompressable then you could use Bernoulli's Equation to say that the pressure of the fluid at any point along the tube would be the same (so long as the area of the tube does not change) after the application of the impluse due to the pump. Isn't this just a description of a longitudinal wave in a fluid, a result of the impluse applied by the pump?
 
Yes, the cross-sectional area of the pipe changes along the x-direction. We would like to study the relationship between the rate of change of pressure and the rate of change of pumping power.

Sarah
 
I think Bernoulli's Equation still applies here. It relates the speed of a fluid to the pressure in the pipe. How are you measuring things?
 

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