Volume Flow Rate, Velocity, Factors

Click For Summary
SUMMARY

The discussion focuses on calculating the decrease in flow rate when a water pipe with a diameter of 20 cm and a flow rate of 10 cm/s splits into two smaller pipes with diameters of 11.54 cm and 16.33 cm. The volume flow rates for the smaller pipes were calculated as 104.59 cm³/s and 209.44 cm³/s, respectively, resulting in a total flow rate of 314.16 cm³/s for the larger pipe. The participants sought clarification on determining the factor by which the flow rate decreases, emphasizing the need for a systematic approach rather than trial and error.

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically the continuity equation.
  • Familiarity with calculating cross-sectional areas of circular pipes.
  • Knowledge of volume flow rate calculations.
  • Basic algebra for solving equations related to flow rates.
NEXT STEPS
  • Study the continuity equation in fluid dynamics to understand flow rate conservation.
  • Learn how to derive flow rates from pipe diameters using the formula Q = A * v.
  • Explore the concept of flow rate distribution in branching pipes.
  • Investigate the effects of pipe diameter on flow velocity and pressure drop.
USEFUL FOR

Students in engineering or physics, fluid dynamics enthusiasts, and anyone involved in hydraulic system design or analysis will benefit from this discussion.

karmatic
Messages
18
Reaction score
0

Homework Statement


By what factor does the flow rate decrease when a water pipe of diameter 20 cm with a 10 cms^-1 flow rate, splits into two smaller pipes of diameters 11.54 cm and 16.33 cm?


Homework Equations


Q(volume flow rate)=(average velocity)(cross sectional area of flow)


The Attempt at a Solution


Q=(10cm/s^-1)(1/4*3.14*(20cm)^2)
Q=314.16cm^3/s

Q=(10cm/s^-1)(1/4*3.14*(11.54cm)^2)
Q=104.59cm^3/s

Q=(10cm/s^-1)(1/4*3.14*(16.33cm)^2)
Q=209.44cm^3/s

Just in case anyone is wondering, the "flow rate" stated in the problem question is actually the velocity (I had to clarify that with my teacher). I think I have the flow rates calculated correctly, but I am unsure of how to go about working out what factor the flow rate is decreasing by for each of the smaller pipes. The answer is a multiple choice question so it was a simple process of trial and error to work out which pair of factors worked for the problem, but is there a way of showing how I would work that out without the multiple choice aspect? I want to be able to show as much working as possible! Thanks in advance :)
 
Physics news on Phys.org
hey man I am actually doing the same question how did u go about the guess and check to find out which one ?
 

Similar threads

Poiseuille equation for water flow rate
  • · Replies 16 ·
Replies
16
Views
3K
Bernoulli equation for calculation of water flow
  • · Replies 30 ·
2
Replies
30
Views
3K
Speed/Velocity and Volume Flow Rate of Viscous Fluids
  • · Replies 5 ·
Replies
5
Views
2K
Calculate flow rate in a tap and the height of a reservoir
  • · Replies 5 ·
Replies
5
Views
3K
Maximum height for water from a fire hose
  • · Replies 4 ·
Replies
4
Views
4K
The Pressure Distribution in a Narrowing Tube with Increasing Fluid Velocity
  • · Replies 10 ·
Replies
10
Views
4K
Fluid Mechanics: Flow rate required to achieve a constant height
  • · Replies 4 ·
Replies
4
Views
2K
What Is the Mass Flow Rate at Exit in a Steady Flow System?
  • · Replies 1 ·
Replies
1
Views
2K
Finding height of buffer regions and viscous sublayer turbulent flow
  • · Replies 4 ·
Replies
4
Views
2K
Why Doesn't the Flow Rate Change When a Vane is Moving in a Pipe?
  • · Replies 11 ·
Replies
11
Views
2K