General equation of velocity along the pipe

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SUMMARY

The discussion focuses on deriving the general equation for fluid velocity in a pipe diffuser where the diameter transitions from 0.5m to 1m over a length of 1m. The principle of continuity is applied, stating that fluid velocity decreases as the pipe diameter increases. The user proposes a formula involving the entrance velocity and the area of the pipe, seeking validation of their approach. The importance of ensuring dimensional correctness in the derived equation is emphasized.

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically the continuity equation.
  • Knowledge of pipe flow characteristics and how diameter affects velocity.
  • Familiarity with basic algebra and dimensional analysis.
  • Experience with fluid mechanics equations and their applications.
NEXT STEPS
  • Study the continuity equation in fluid dynamics to solidify understanding of velocity changes in varying pipe diameters.
  • Explore the derivation of the Bernoulli equation and its application in pipe flow scenarios.
  • Investigate dimensional analysis techniques to ensure the correctness of fluid mechanics equations.
  • Learn about practical applications of pipe diffusers in engineering and their impact on fluid flow efficiency.
USEFUL FOR

Students studying fluid mechanics, engineers working on pipe design, and anyone involved in fluid flow analysis in piping systems.

foo9008
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Homework Statement


A pipe diameter changes from 0.5m to 1m in a length of 1m in a pipe diffuser . If a discharge Q flows from 0.5m diameter towards 1m diamater , obtain the general expression for velocity at the pipe cross section .

Homework Equations

The Attempt at a Solution


since we know that the velocity of fluid in pipe decreases when the size of pipe increases , So , my working is Velocity at the entrance - (difference in velocity between entrance and exit / area of pipe ) , where the area of pipe has the diameter which increases from the entrance ) , i let is as x in my working . Is my working correct ?
 

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You can simply use equation of continuity.
Check if your equation is dimensionally correct.
 
foo9008 said:

Homework Statement


A pipe diameter changes from 0.5m to 1m in a length of 1m in a pipe diffuser . If a discharge Q flows from 0.5m diameter towards 1m diamater , obtain the general expression for velocity at the pipe cross section .

Homework Equations

The Attempt at a Solution


since we know that the velocity of fluid in pipe decreases when the size of pipe increases , So , my working is Velocity at the entrance - (difference in velocity between entrance and exit / area of pipe ) , where the area of pipe has the diameter which increases from the entrance ) , i let is as x in my working . Is my working correct ?
I just see a diagram. If there is any working associated with it, it is not visible.
 
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SteamKing said:
I just see a diagram. If there is any working associated with it, it is not visible.
sorry , here is it
 

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