Turbulent flow velocity profiles

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SUMMARY

The discussion focuses on calculating turbulent flow velocity profiles in ducts and pipes using the formula vy/vy=0 = (1-y/r)1/7. For air flowing in a duct with a diameter of 0.6m and water in a pipe with a diameter of 0.5m, both at a Reynolds number (Re) of 105, participants are tasked with plotting velocity profiles and calculating mean velocities (vmean) and velocity at the centerline (vy=0). Additionally, the Blasius equation is applied to determine friction factor (f) and pressure drop per unit length (ΔP/L) for the duct flow. Kinematic viscosity values must be sourced from textbooks or online resources.

PREREQUISITES
  • Understanding of turbulent flow dynamics
  • Familiarity with Reynolds number calculations
  • Knowledge of the Blasius equation for friction factor
  • Ability to plot velocity profiles using mathematical formulas
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  • Research how to calculate kinematic viscosity for air and water
  • Learn about plotting velocity profiles in fluid dynamics
  • Study the implications of Reynolds number on flow characteristics
  • Explore advanced applications of the Blasius equation in engineering
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Students in fluid mechanics, engineers working with fluid dynamics, and researchers analyzing turbulent flow characteristics in ducts and pipes.

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i've been given this question by my lecturer at university and I am struggling with where to start with it to be honest. it feels like i don't have enough information. please can someone help?

For turbulent flow, the velocity profile inside a duct and a pipe of diameters Dd and Dp and
both with distance y from the centre line is: vy/vy=0 = (1-y/r)1/7, where vy=0 = vmean/0.817 and vmean=Q/A. Plot the velocity profiles for:

(a) Air flowing in a duct measuring Dd = 0.6m and with Re = 105.
(b) Water flowing in a pipe measuring Dp = 0.5m and with Re = 105.
(c) Calculate the vmean and vy=0 for both cases (a) and (b)
(d) If the Blasius equation f = 0.079Re-0.25 applies, calculate the values of f and ΔP/L for (a)
 
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