Equation of continuity - what if more openings are added?

[RUphysics3]

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?

 

[FactChecker]

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.

 

[RUphysics3]

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

 

[FactChecker]

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.

 

[RUphysics3]

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?

 

[FactChecker]

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.