[Conceptual Question] Fluid Mechanics Analysis of Pipe Flow

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SUMMARY

The discussion centers on the impact of vertical displacement of a pipe network on the volume flow rate in fluid mechanics. Specifically, it concludes that the elevation head is primarily related to the free surface height of the water in the tank rather than the entrance or exit positions of the pipes. The relevant equations for this analysis include the head loss equation Hf=f L/d V^2/g and the head loss due to fittings Hl= K V^2/g. The key takeaway is that the elevation head drives the flow, emphasizing the importance of the free surface height in calculations.

PREREQUISITES
  • Understanding of fluid mechanics principles
  • Familiarity with head loss equations in pipe flow
  • Knowledge of the relationship between elevation head and flow rate
  • Basic concepts of flow dynamics and pipe network design
NEXT STEPS
  • Study the derivation and application of the Darcy-Weisbach equation for head loss
  • Learn about the impact of pipe entrance and exit conditions on flow characteristics
  • Explore the concept of hydraulic grade line and its significance in fluid systems
  • Investigate the effects of pipe diameter and length on flow rate and head loss
USEFUL FOR

This discussion is beneficial for students and professionals in mechanical engineering, civil engineering, and fluid dynamics, particularly those focusing on pipe flow analysis and hydraulic systems design.

aerograce
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Homework Statement


As shown in the figure, if the pipe net work is shifted bodily by 10m vertically up the tank, and all the other conditions remain the same as the previous figure. Will the volume flow rate change?

Or I rephrase it as, in the calculation of elevation head of pipe flow, is the elevation head related to free surface height of the water in tank, or the entrance/exit position of the pipes from the tank?

Homework Equations


Relevant Equations are:
Hf=f L/d V^2/g
Hl= K V^2/g

The Attempt at a Solution


The attempt at this problem is:
I think it is related to free surface height of the water in tank only since in calculation we usually draw a line from one water tank free surface to another.
 

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You are correct (if I understand you correctly). The flow entrance distance below the free surface is the key factor since it is this head that drives the flow. In the first figure, the entrance appears to be somewhat close to the tank bottom, and that could have a minor effect on the nature of the flow around the entrance, but the big factor is the head.
 

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