Equation of continuity - what if more openings are added?

In summary: The equation A1V1 = A2V2 holds true in all situations, including the case of a showerhead with 20 openings. This is because the total flow in must equal the total flow out, so A1V1 (the area and velocity of the water flowing in) must equal A2V2 (the area and velocity of the water flowing out). Therefore, there is no need to divide by 20, as A2 already takes into account the total area of all 20 openings. In summary, the equation A1V1 = A2V2 holds true for all situations, including the case of a showerhead with 20 openings, because the total flow in must equal the total flow out, and A
  • #1
RUphysics3
24
0
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?
 
Physics news on Phys.org
  • #2
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.
 
  • Like
Likes RUphysics3
  • #3
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
 
  • #4
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.
 
  • #5
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?
 
  • #6
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.
 

Related to Equation of continuity - what if more openings are added?

1. How does adding more openings affect the equation of continuity?

Adding more openings does not affect the equation of continuity. The equation remains the same regardless of the number of openings. The equation simply states that the mass flow rate into a system equals the mass flow rate out of the system.

2. Will the mass flow rate increase or decrease if more openings are added?

The mass flow rate will increase if more openings are added. This is because more openings provide more pathways for fluid to enter or exit the system, resulting in a higher mass flow rate.

3. Does the shape or size of the openings affect the equation of continuity?

No, the shape or size of the openings does not affect the equation of continuity. The equation only considers the total mass flow rate into and out of the system, not the specifics of the openings.

4. Can the equation of continuity be applied to any type of fluid?

Yes, the equation of continuity can be applied to any type of fluid, whether it is a liquid or a gas. This is because the equation is based on the principle of conservation of mass, which applies to all types of fluids.

5. How is the equation of continuity related to conservation of mass?

The equation of continuity is directly related to the principle of conservation of mass. It states that the total mass entering a system must equal the total mass exiting the system, in order to maintain the principle of conservation of mass. This is why the equation is often used in fluid mechanics, where the movement of fluids must adhere to the principle of conservation of mass.

Similar threads

  • Introductory Physics Homework Help
Replies
8
Views
3K
  • Other Physics Topics
Replies
13
Views
3K
  • Introductory Physics Homework Help
Replies
1
Views
5K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
3K
Replies
7
Views
2K
  • Mechanical Engineering
Replies
4
Views
1K
  • Other Physics Topics
Replies
2
Views
1K
Replies
14
Views
371
  • Introductory Physics Homework Help
Replies
7
Views
4K
Back
Top