Flow Rate in Pipe: Q, v, A Explained

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Discussion Overview

The discussion revolves around the flow rate in a pipe, specifically the relationship defined by the equation Q = v * A, where Q is the flow rate, v is the fluid velocity, and A is the cross-sectional area of the pipe. Participants explore the implications of this equation in practical scenarios, including the effects of friction losses and pressure on flow rate, as well as the limitations of the equation in real-world applications.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant asserts that flow rate depends solely on the inner area of the pipe and fluid velocity, suggesting that pressure loss does not affect flow rate until a certain point.
  • Another participant agrees that a pump's limited power could affect the flow rate due to friction losses, questioning whether unlimited power would maintain a constant flow rate.
  • A participant introduces a more complex equation for incompressible fluid flow, indicating that pressure drop adjusts to maintain a fixed volume flow rate.
  • One comment emphasizes that while an equation may not include pressure, it does not imply pressure is irrelevant; it highlights the need to understand the context of equations in real-world applications.
  • Several participants note that the original equation applies ideally and that real-world factors such as friction must be considered for accurate flow rate calculations.
  • Another participant points out that the relationship between flow rate and pressure drop is critical in designing fluid systems.

Areas of Agreement / Disagreement

Participants generally agree that flow rate is influenced by factors beyond just area and velocity, particularly friction and pressure. However, there is no consensus on the extent to which these factors affect the flow rate or how they should be integrated into calculations.

Contextual Notes

Some limitations are noted regarding the assumptions made in the original equation, particularly in relation to ideal versus real-world scenarios, and the dependence on specific definitions of flow conditions.

Who May Find This Useful

This discussion may be useful for individuals interested in fluid dynamics, engineering applications related to piping systems, or those studying the principles of fluid mechanics.

AdrianTTT
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Hi,

I have a question regarding the flow rate in a pipe. According to the general rule the flow rate is:

Q = v * A

where Q [m3/s]
v [m/s]
A [m2]

So according to this formula the flow rate depends only on the inner area of the pipe and the velocity of the fluid and does not matter what the pressure loss is until a certain point. So I had this argument this other day with someone and he said that the flow rate depends on the friction losses in the pipe. But I don't see where that happens according to this formula. If I have a pump that provides 2 [m3/h] and there is only one pipe, no matter how long or how many curves it makes the water flow at the end of the pipe will still be 2 [m3/h] because no mass is lost anywhere if there is no ramification.
The only doubt that I have is that the pump might not be able to provide 2 [m3/h] because it has limited power therefore it will soon succumb to the accumulating friction losses in the pipe therefore the declining flow rate. But if the pump would have unlimited power then the flow rate would remain the same right ? Anyway I could not find the relation between the friction losses, power and flow rate and how this all comes together in an elegant explanaition and if someone could provide one it would be much appreciated. Thanks!
 
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AdrianTTT said:
the pump might not be able to provide 2 [m3/h] because it has limited power therefore it will soon succumb to the accumulating friction losses in the pipe
Good understanding.
AdrianTTT said:
unlimited power then the flow rate would remain the same right ?
Another good understanding.
For an incompressible fluid flow rate through a straight tube of constant radius (diameter) is given by

(dV/dt) = (πr4ΔP)/(8ηL), where "r" is the radius of the tube/pipe, "L" is the length, "ΔP" is the difference in pressure between inlet and outlet of the tube, and "η" is the viscosity of the fluid.

Do you want to go into more detail?
 
To expand on what Bystander said, if you fix the volume flow rate (and the fluid is incompressible), the pressure drop in the pipe will adjust itself to conform to this.

Chet
 
Just a comment on the root cause of the issue: this is a matter of not understanding how equations apply to the real world (a common issue). An equation means what it says and nothing more. If it doesn't include pressure, that does NOT mean pressure is irrelevant in all cases involving flow, it just means that the person who wrote the equation decided to focus on describing something else. The equation relates three quantities and IF you know two you can find the third, but it doesn't say where you got them.

Consider two types of flow meters:
A turbine flow meter measures flow velocity using a spinning paddle wheel. So you need only the pipe diameter and that equation to find the flow rate.

A pito array measures pressure, so you need Bernoulli's equation to find the velocity, THEN you can use Q=VA to find flow rate.

So yes, pressure definitely matters for fluid flow, but whether it enters a particular problem depends on the problem.
 
Thanks for your answers, I guess the flow rate does in fact depend on more than just flow area and velocity... I'm guessing that the formula above can be applied directly only for ideal cases, no friction with pipe, between particles etc., otherwise I need to find the flow by other means.
 
Last edited:
Hey, you did fine understanding that mass had to be conserved between the inlet and outlet of the pipe, and understanding that the longer the pipe, the harder the pump has to work to maintain flow rate. The rest of the bookkeeping on flow problems is NOT so obvious.
 
AdrianTTT said:
Thanks for your answers, I guess the flow rate does in fact depend on more than just flow area and velocity... I'm guessing that the formula above can be applied directly only for ideal cases, no friction with pipe, between particles etc., otherwise I need to find the flow by other means.
That's not what I said, and it applies much more widely than just ideal cases.

Chet
 
Right: Q=VA is a very small piece of a much larger problem. When designing a fluid duct/piping system, pressure drop/rise plays a critical role.
 

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