Equation of continuity - what if more openings are added?

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Discussion Overview

The discussion revolves around the application of the equation of continuity in fluid dynamics, specifically in scenarios where a single pipe opens into multiple outlets, such as a showerhead. Participants explore how to interpret the equation A1V1 = A2V2 when considering multiple openings and the implications for flow rates and areas.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions whether the equation should be modified to A1V1 = A2V2/20 in the case of multiple openings.
  • Another participant asserts that A2 represents the total area of all openings combined, regardless of the number of holes, emphasizing that total flow in equals total flow out.
  • A later reply reiterates that A2 is the total area of all openings, and suggests that the velocity v2 is uniform across all openings if they have equal areas.
  • One participant references an external source to clarify the application of the equation in a specific problem, questioning the use of a division by 20.
  • There is a confirmation of understanding that A2 is the combined area of all openings and that the velocity is consistent across them.

Areas of Agreement / Disagreement

Participants generally agree that A2 should be considered as the total area of all openings combined, but there is some uncertainty regarding the interpretation of the equation in relation to the number of openings and whether any modifications are necessary.

Contextual Notes

Some assumptions about the uniformity of flow and the equal area of openings are present, but these are not explicitly resolved in the discussion.

Who May Find This Useful

Individuals interested in fluid dynamics, particularly in understanding the application of the equation of continuity in practical scenarios involving multiple outlets.

RUphysics3
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The equation states that A1V1=A2V2. What about in a situation like a showerhead, where it's one long pipe/tube, then opens up to say, 20 holes. Is it now A1V1=A2V2/20 ? why/why not?
 
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A2 is the total area, regardless of how many holes it is divided up into. That is because over any length of time, the total flow in equals the total flow out. So don't divide by 20.
 
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There are 20 holes, each with an area of (10-3m)2, so the total area of all 20 of them is A2 = 20*(10-3m)2. So the equation (shown on the first line of the answer) is still A1V1 = A2V2.
 
okay, so A2 , if there are 20 openings, is the area of ALL 20 openings, while v2 is the speed of the liquid out of one of the openings, which is uniform through all twenty of them as they are equal areas?
 
RUphysics3 said:
okay, so A2 , if there are 20 openings, is the area of ALL 20 openings, while v2 is the speed of the liquid out of one of the openings, which is uniform through all twenty of them as they are equal areas?
That sounds right to me.
 

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