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

[cheertcc101]

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!

 

[FredGarvin]

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 $$A=\frac{1}{4}\pi*D^2$$

 

[baba89]

I can provide the following response to the Reynolds number problem:

1. Effect of increasing mass flow rate on Re: As the mass flow rate increases, the Reynolds number will also increase. This is because the Reynolds number is directly proportional to the velocity of the flow, which is affected by the mass flow rate. Therefore, as mass flow rate increases, the velocity and intensity of the flow also increase, resulting in a higher Reynolds number. This can potentially lead to a transition from laminar to turbulent flow, depending on the specific values of the other parameters.

2. Effect of increasing D on Re: When the pipe diameter increases, the Reynolds number will decrease. This is because the Reynolds number is inversely proportional to the pipe diameter. As the diameter increases, the velocity of the flow decreases, resulting in a lower Reynolds number. This means that the flow is more likely to be in the laminar regime. However, if the mass flow rate is also increased, it can counteract the decrease in Reynolds number and potentially lead to turbulent flow. Additionally, if the dynamic viscosity (mu) is also increased, it can further decrease the Reynolds number and maintain laminar flow.