Why is the force on the fluid not equal to the change in momentum per unit time?

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SUMMARY

The discussion focuses on the relationship between fluid momentum and the forces acting on it in a pipe with a right-angle bend. It establishes that the force on the fluid is not simply the change in momentum per unit time but rather the vector difference of the momentum flows. The calculations demonstrate that the rate of change of momentum in both horizontal and vertical directions is influenced by the pipe walls, with specific examples provided for a 45-degree bend using water density and flow velocity. The conversation emphasizes the importance of understanding control volumes and the assumptions of incompressible flow.

PREREQUISITES
  • Understanding of fluid dynamics principles, specifically momentum flow.
  • Familiarity with control volume analysis in fluid mechanics.
  • Knowledge of Bernoulli's equation and its applications.
  • Basic mathematical skills for calculating forces and momentum changes.
NEXT STEPS
  • Study the control volume approach in fluid dynamics.
  • Learn about Bernoulli's equation and its implications for fluid flow in pipes.
  • Explore the concept of the material derivative in fluid mechanics.
  • Investigate the effects of compressible versus incompressible flow on momentum calculations.
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Fluid mechanics students, engineers designing piping systems, and anyone involved in analyzing fluid flow dynamics in various applications.

  • #31
Vibhor said:
Chet , I understand your point . Just help me understand why in the books it is written that horizontal force exerted by fluid on pipe is ##\rho v^2A## . Are there any assumptions involved or am I misinterpreting something ?
Maybe they are assuming that the fluid pressure in the pipe is just atmospheric pressure (zero gage), or maybe they just inadvertently left out the pressure force.
 

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