Deriving Discharge Expression for Broad Crested Weir Model

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SUMMARY

The discussion focuses on deriving the discharge expression for a broad crested weir model using the Buckingham Pi theorem. The key variables involved are the spillway head (H), gravitational acceleration (g), and spillway height (h). It is established that discharge (Q) cannot be chosen as a repeating variable in the dimensional analysis since it is a dependent variable, while H and g serve as the appropriate repeating variables. This conclusion is critical for accurately modeling the discharge characteristics of the weir.

PREREQUISITES
  • Understanding of the Buckingham Pi theorem
  • Familiarity with fluid mechanics concepts
  • Knowledge of dimensional analysis
  • Basic principles of weir flow and discharge equations
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Homework Statement


A broad crested weir model is designed to study the discharge per meter of the prototype. Derive an expression for this discharge using the Buckingham Pi theorem. Assume that the overflowing water sheet is thick so that the surface tension and thus viscosity of the fluid can be neglected. The equation of discharge (Q) for a weir has related with a function of spillway head (H), the gravitational acceleration (g), and the spillway height (h)

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The Attempt at a Solution



in this question , Q (discharge ) can't be chosen as repeating variable , right ? the repeating variables should be H and g , Am i right ? [/B]
 
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since Q is the dependent variable , am i right ?
 

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