Need help with a Bernoulli(?) expression

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    Bernoulli Expression
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Discussion Overview

The discussion revolves around the interpretation of the expression "PV + mgh + 0.5mv^2 = constant" and its relation to Bernoulli's equation. Participants are exploring the meaning of the expression in the context of fluid dynamics, specifically regarding conservation of energy principles and the conditions under which Bernoulli's equation applies.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest that the expression reflects conservation of energy principles, with options including conservation per volume unit or mass unit.
  • Others argue that the expression is not the Bernoulli equation as traditionally understood, questioning the definitions of variables like m, V, and h.
  • A participant mentions that dividing the expression by volume leads to a form resembling Bernoulli's equation, suggesting it could be a trick question to test recognition of the equation.
  • Some participants express uncertainty about the physical meaning of manipulating the equation, particularly regarding the implications of multiplying through by volume.
  • There are discussions about kinetic and potential energy being forms of energy, and how these relate to the terms in the expression.
  • A participant notes that the expression could be used to describe scenarios like hydroelectric dams, linking it back to conservation of energy.
  • Another participant proposes that the question may be designed to challenge students' understanding of Bernoulli's equation in a different context.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct interpretation of the expression or which answer choice is correct. Multiple competing views remain, with some favoring options related to conservation of energy and others questioning the validity of the expression as a representation of Bernoulli's equation.

Contextual Notes

Participants note the lack of information regarding units in the original question, which may affect interpretations. There is also mention of assumptions related to the conditions under which Bernoulli's equation is valid, such as incompressibility and absence of friction.

Rajasti
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Hello! So this is my problem here, there's a question I've been studying for an exam in which I really can't understand the answer. Basically it has multiple choices and I'm very undecided. So this is it:

Expression: "What does this expression reflect? PV + mgh + 0,5mv^2 = constant "

a) Conservation of energy per volume unit, within an ideal fluid;
b) Conservation of energy per mass unit, within a Newtonian fluid;
c) Conservation of energy for an incompressible fluid;
d) None of the above. It's simply Bernoulli's Equation;

Which one is correct? Please help!
 
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Rajasti said:
Hello! So this is my problem here, there's a question I've been studying for an exam in which I really can't understand the answer. Basically it has multiple choices and I'm very undecided. So this is it:

Expression: "What does this expression reflect? PV + mgh + 0,5mv^2 = constant "

a) Conservation of energy per volume unit, within an ideal fluid;
b) Conservation of energy per mass unit, within a Newtonian fluid;
c) Conservation of energy for an incompressible fluid;
d) None of the above. It's simply Bernoulli's Equation;

Which one is correct? Please help!
What are the units of the equation?
 
This is all the question description has. No mention of units of any kind :/
 
Rajasti said:
This is all the question description has. No mention of units of any kind.
You can just pick a system of units, such as metric units, and see how that effects the equation you have.
 
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Rajasti said:
Hello! So this is my problem here, there's a question I've been studying for an exam in which I really can't understand the answer. Basically it has multiple choices and I'm very undecided. So this is it:

Expression: "What does this expression reflect? PV + mgh + 0,5mv^2 = constant "
Where did you get this equation from? It is definitely not the Bernoulli equation as I know it. What is m, V, and h in your relationship?
 
Chestermiller said:
Where did you get this equation from? It is definitely not the Bernoulli equation as I know it. What is m, V, and h in your relationship?
Looks like they multiplied-through by volume (V)?
 
russ_watters said:
Looks like they multiplied-through by volume (V)?
What does it even mean physically to do something like that?
 
Well, believe it or not, this weird question has been present in my teacher's exam several years now. And today I'm having this exam and I'm afraid this crappy question comes up. I've asked here, reddit, asked physics friends. I've had some say is A), some say it's D). I am desperate here, and at this point Imma have to risk one of them through intuition or something. Can't seem to unite a consensus :(
 
What it seems to me is cinetic energy (0,5mv^2), potencial energy (mgh) and something relates to energy in PV as in Pressure * Volume. But I have no idea what this is either.
 
  • #10
A friend of mine said that if you divide this expression by V, you get P + rhogh + 1/2rhov^2, this because rho (specific mass) = m(mass) / V (volume) and then you get Bernoulli equation. So he said maybe D). Just a stupid way for the teacher to test if we recognize Bernoulli equation in a slightly different setting...
 
  • #12
Rajasti said:
Hello! So this is my problem here, there's a question I've been studying for an exam in which I really can't understand the answer. Basically it has multiple choices and I'm very undecided. So this is it:

Expression: "What does this expression reflect? PV + mgh + 0,5mv^2 = constant "

a) Conservation of energy per volume unit, within an ideal fluid;
b) Conservation of energy per mass unit, within a Newtonian fluid;
c) Conservation of energy for an incompressible fluid;
d) None of the above. It's simply Bernoulli's Equation;

Which one is correct? Please help!

I've read/laerned about at least three ways to obtain the Bernoulli equation, one of them was to derive it by starting with the conservation of energy of an incompressible fluid without losses (friction). So for me answer c) could be the right one. Dividing it by the volume yields the "classic" Bernoulli equation, every pupil hears about in school.

EDIT: ..and of course no heat transfer.
 
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  • #13
Rajasti said:
What it seems to me is cinetic energy (0,5mv^2), potencial energy (mgh) and something relates to energy in PV as in Pressure * Volume. But I have no idea what this is either.
And both kinetic and potential energy are forms of_____? C'mon, I think I know what the teacher is getting at and it really is that easy!

Next, since it is obviously at least related to Bernoulli's equation, what are the required assumptions/constraints on Bernoulli's equation?
Rajasti said:
Just a stupid way for the teacher to test if we recognize Bernoulli equation in a slightly different setting...
I think that is the purpose and if so, the fact that you and your classmates are having so much trouble with it proves it isn't a stupid question but a necessary one!
 
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  • #14
Chestermiller said:
What does it even mean physically to do something like that?
You might use this [nearly]exact equation (with or without a time factor) to describe the function of a hydroelectric dam, for example. As @stockzahn pointed out, this just takes Bernoulli's equation back to the conservation of energy statement it came from (you can view it from either direction).
 
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  • #15
I thought the answer was given away already, but since there are still questions, try eliminating wrong options. If you used my suggestion of using metric units for the terms of the equation is each term a value of a) energy per unit volume or b) energy per unit mass or c) just energy?
 

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