Rate of flow, or velocity of fluid?

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Discussion Overview

The discussion revolves around the terminology used to describe fluid dynamics, specifically the concepts of "rate of flow" and "velocity" in the context of water pressure and flow from holes in a container. Participants explore the implications of these terms in relation to fluid mechanics principles, particularly under conditions of laminar flow and neglecting frictional forces.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants assert that "rate of flow" is often confused with "velocity," suggesting that the author likely intended to refer to velocity when discussing the flow from smaller holes.
  • Others argue that the terms "flow rate" and "rate of flow" are ambiguous and could refer to different concepts, such as volumetric flow rate or mass flow rate, making it unclear what the author meant.
  • One participant emphasizes that if the holes are of equal size, then variations in flow velocity must correspond to differences in mass or volumetric flow for liquids.

Areas of Agreement / Disagreement

Participants generally agree that the terminology used is ambiguous and that this ambiguity can lead to confusion regarding the intended meaning. However, there is no consensus on the correct interpretation of the author's statement.

Contextual Notes

The discussion highlights limitations in the clarity of terminology used in fluid dynamics, particularly regarding the definitions of flow rate and velocity. The implications of these terms depend on specific conditions such as the nature of the flow (laminar vs. turbulent) and the assumptions made about frictional forces.

Doug1943
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I was looking at a site which described the classic demonstration to illustrate how water pressure increases with depth (shown by punching three holes, one above the other separated by a few centimeters, in a container of water): "The smaller the holes, the greater the rate of flow from the holes."

Is this right? Does not the author mean, "The smaller the holes, the greater the velocity of the water"? (I think of "rate of flow" as being total volume passing a point per unit time, which must remain constant. And presumably these relationships only hold when the flow is laminar and frictional forces are neglected?)
 
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I believe you are correct, the author meant velocity. Otherwise the continuity equation would be violated.

cross sectional area x velocity = constant
 
It depends on what the author said. If he/she just said "flow rate" or "rate of flow", those are ambiguous terms and so they may have simply meant velocity rather than volumetric flow rate or mass flow rate. In other words, they may have been right or wrong but you can't really tell because the terminology as you describe it is ambiguous.
 
If the holes are equal in size, then different flow velocity necessarily means different mass/volumetric flow, for liquids.
 

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