Equation of continuity - what if more openings are added?

Click For Summary
SUMMARY

The equation of continuity, expressed as A1V1 = A2V2, applies regardless of the number of openings in a system. In the case of a showerhead with 20 holes, A2 represents the total cross-sectional area of all openings combined, calculated as A2 = 20*(10^-3 m)^2. The velocity of the fluid exiting each hole, denoted as V2, remains uniform across all openings due to equal area distribution. Therefore, the equation does not require division by the number of holes.

PREREQUISITES
  • Understanding of fluid dynamics principles
  • Familiarity with the equation of continuity
  • Basic knowledge of cross-sectional area calculations
  • Concept of uniform flow in fluid systems
NEXT STEPS
  • Study the derivation and applications of the equation of continuity in fluid dynamics
  • Explore the concept of uniform flow and its implications in various fluid systems
  • Investigate how to calculate total cross-sectional area for multiple openings
  • Learn about Bernoulli's principle and its relationship to fluid flow
USEFUL FOR

Students of physics, engineers in fluid mechanics, and anyone interested in understanding fluid flow in systems with multiple outlets.

RUphysics3
Messages
24
Reaction score
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
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   Reactions: RUphysics3
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.
 

Similar threads

Undergrad Help Understanding Volume Flow Rate / Bernoulli's
  • · Replies 1 ·
Replies
1
Views
5K
Fluid Dynamics: Solving the Equation of Continuity
  • · Replies 8 ·
Replies
8
Views
4K
Undergrad Continuity of Hamiltonian at separatrix in action-angle variables
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Multistage continuous Rocket Eqn
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Different answers from equation of continuity and Bernoulli
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Bernoulli's Equation & Equation of Continuity
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad Equation of Continuity: Leaking Bucket & Minus Sign
  • · Replies 13 ·
Replies
13
Views
3K
Bernoulli/Continuity, Water flowing at different heights/radii
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad Find Best Water Nozzle Type & Pressure for Longest Distance
  • · Replies 32 ·
2
Replies
32
Views
10K
Undergrad Boundary conditions for a stream function in a hydrodynamics problem
  • · Replies 5 ·
Replies
5
Views
1K