How Does Changing Mass Flow Rate or Diameter Affect Reynolds Number?

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SUMMARY

The Reynolds number (Re) is a dimensionless quantity that indicates flow characteristics, defined by the equation Re = u(density)D/mu, where D represents pipe diameter and mu is dynamic viscosity. Increasing mass flow rate while keeping diameter and viscosity constant results in a higher Reynolds number, indicating a transition from laminar to turbulent flow. Conversely, if mass flow rate and viscosity are held constant, increasing the diameter (D) also raises the Reynolds number due to the direct relationship between diameter and flow intensity. Understanding these relationships is crucial for fluid dynamics analysis.

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  • Understanding of fluid dynamics principles
  • Familiarity with the Reynolds number and its significance
  • Knowledge of mass flow rate calculations
  • Basic grasp of pipe flow characteristics
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The question gives this ..

The Reynolds number, Re, is a dimensionless group which characterizes the intensity of a flow. For large Re, a flow is turbulent; for small Re , it is laminar. For pipe flow, Re=u(density)D/mu, where D is pipe diameter and mu is dynamic viscosity.

It asks ..

If D and mu are fixed, what is the effect of increasing mass flow rate on Re?
and
If mass flow rate and mu are fixed, what is the effect of increasing D on Re?

Any help is appreciated,

Thanks!
 
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First of all, while Re is used to characterize the type of flow, it is a ratio of forces in a flowing fluid. It is a ratio of the inertial forces to the viscous forces.

Start by looking at what defines the mass flow rate...\dot{m}=\rho*A*V

You'll also need to look at the fact that area is A=\frac{1}{4}\pi*D^2
 

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