Fluid Mechanics, Drag Coefficient of a Cylinder

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SUMMARY

The discussion focuses on calculating the pressure drag coefficient (Cdp) for a cylinder using the trapezoidal and Simpson's rules. The provided data includes pressure coefficients (Cp) at various angles, with values ranging from 1 at 0 degrees to -1.288 at 180 degrees. The equation Cdp = 0.5 ∫ Cp cos∅ d∅ is central to the calculations. Participants seek clarification on applying numerical integration methods to the given data, specifically how to set up the function values and intervals for accurate results.

PREREQUISITES
  • Understanding of fluid mechanics principles, specifically drag coefficients.
  • Familiarity with numerical integration techniques, particularly trapezoidal and Simpson's rules.
  • Knowledge of pressure coefficients and their significance in fluid dynamics.
  • Ability to convert degrees to radians for mathematical calculations.
NEXT STEPS
  • Research the application of the trapezoidal rule in numerical integration.
  • Study Simpson's rule for approximating integrals in fluid mechanics.
  • Explore the significance of pressure coefficients (Cp) in calculating drag forces.
  • Learn about the conversion of angles from degrees to radians in mathematical contexts.
USEFUL FOR

Students and professionals in engineering, particularly those specializing in fluid mechanics, as well as anyone involved in computational fluid dynamics and drag force analysis.

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Homework Statement



Calculate the pressure drag cofficient for a cylinder using the trapezoidal and simpson's rule (assume the flow is the same on both sides of the cylinder).

Angle (deg) Cp
0 1
30 0.274
60 -1.565
90 -1.3
120 -1.288
150 -1.288
180 -1.288


Homework Equations



Cdp = 0.5 ∫ Cp cos∅ d∅


The Attempt at a Solution



How do we apply the given data in trapezoidal & simpson's rules?
Which number represents the first value of the function (y)?
 
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I would change degree to radians. Looks like there a n=6 intervals

f(X0)=1 and f(X6)= -1.288 for both trapezoidal and Simpson's rule

Google if you don't know how to apply these rules. I like patrickJMT website for explanations.
 

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