FLUID MECHANICS QUESTION: Froude's Number

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SUMMARY

The discussion focuses on calculating the actual flow for a prototype spillway using Froude's Number and dimensional analysis. The model spillway has a flow rate of 100 L/s per meter, and the scale ratio is 1:20. The key equation used is qr = qp/qm, where qm is the model flow rate of 0.1 m³/s per meter. The user seeks to determine the velocity (Vr) of the prototype to compute the actual flow (qp) for the prototype spillway.

PREREQUISITES
  • Understanding of fluid mechanics principles, specifically Froude's Number.
  • Knowledge of dimensional analysis and scale modeling.
  • Familiarity with flow rate equations in fluid dynamics.
  • Basic algebra for solving equations related to flow rates.
NEXT STEPS
  • Research the application of Froude's Number in hydraulic modeling.
  • Learn about dimensional analysis in fluid mechanics.
  • Study the relationship between flow rate, velocity, and cross-sectional area.
  • Explore case studies involving prototype and model comparisons in spillway design.
USEFUL FOR

Students and professionals in civil engineering, particularly those specializing in hydraulic engineering and spillway design, will benefit from this discussion.

KAISER91
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Homework Statement



A model spillway has a flow of 100 L/s per m of width. What is the actual flow for the
prototype spillway if the model scale is 1:20?

Homework Equations



qr = qp/qm

The Attempt at a Solution



My attempt;


qm = 100 L/s per m = 0.1 m^3/s per m


Using the length scale ratio: Lr = Lp/Lm = 20/1 = 20




q = Q/b = VA/b = byV/b = yV

therefore, q = yV
hence, qr = yr Vr

yr = Lr which is 20

So how do I get Vr?
 
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Once I know Vr, I will get qr

Then I can resolve the flow for the prototype using this;

qr = qp/qm

qp = qr x qm


with qm given as 0.1
 

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