I Equation of continuity - what if more openings are added?

AI Thread Summary
The equation of continuity, A1V1 = A2V2, applies regardless of the number of openings, as A2 represents the total area of all openings combined. In the case of a showerhead with multiple holes, A2 is calculated by summing the areas of each hole, not dividing by the number of holes. The flow rate remains consistent, meaning the total flow in equals the total flow out over time. The velocity of the liquid exiting each hole (v2) is uniform if the holes have equal areas. Thus, the equation holds true without the need for division by the number of openings.
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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FactChecker said:
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.
why did they put a twenty at the bottom here,

http://www.physics.rutgers.edu/ugrad/124/Resources/124s16h2-solutions.pdf

number 8
 
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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