# Fluid dynamics: Reynolds Number, Drag Constant

• AwfulPhysicist
In summary, the conversation discusses two queries related to the use of Reynolds number and drag constant in solving a physics problem. It is mentioned that the velocity and dynamic viscosity must be considered separately when using Reynolds number, and that the Reynolds number may vary due to changes in the drag constant. The use of a graph or table is suggested for finding the Reynolds number.

#### AwfulPhysicist

I completed 4a successfully, and with 4b, i have 2 queries:
a)why can't I let Reynolds # equal to 2.19 x 10^5 (from part a) then simply sub v=4 instead of 5m/s and rearrange for viscosity? I tried it this way first and got a very wrong answer. Why do we, essentially, need to work backwards to get the dynamic viscosity?
b)How do they find the reynolds number from the drag constant? I know they used the table but how?

Below is proof of my workings, and i have screen shotted the question and the answer workings as well.

Relevant equations are

F (drag)= drag constant (Cd) x pi/4 x d^2 x density fluid x velocity^2 x 1/2

Reynolds number= (density of fluid x diameter of spehere x velocity)/viscosity

F (drag) = Weight- Buoyancy
= pi/6 x d^3 x gravity x (density of sphere-density of fluid)

kinematic viscosity= dynamic viscoity/ density

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AwfulPhysicist said:
I completed 4a successfully, and with 4b, i have 2 queries:
a)why can't I let Reynolds # equal to 2.19 x 10^5 (from part a) then simply sub v=4 instead of 5m/s and rearrange for viscosity?
I tried it this way first and got a very wrong answer. Why do we, essentially, need to work backwards to get the dynamic viscosity?

Because the velocity also appears in the ##\rho v^2/2## term. So here, it does not appear in combination with the dynamic viscosity.
b)How do they find the reynolds number from the drag constant? I know they used the table but how?

You either plot the relationship on a graph, and use the graph (preferrably a log-log plot) to get the reynolds number, or you interpolate (preferrably logarithmically) in the table.

Chet

Thanks Chet, I also realized that Reynolds number will not be the same due to a variation in the drag constant. So we cannot use the same Reynolds number as the first part

## 1. What is the Reynolds Number in fluid dynamics?

The Reynolds Number is a dimensionless quantity used to predict the type of flow in a fluid, based on its velocity, density, and viscosity. It is calculated by dividing the product of velocity, length, and density by the dynamic viscosity of the fluid.

## 2. How is the Reynolds Number related to fluid flow?

The Reynolds Number is used to determine whether a fluid flow is laminar or turbulent. Laminar flow occurs at low Reynolds Numbers, while turbulent flow occurs at high Reynolds Numbers. This relationship is important in understanding the behavior of fluids in various applications.

## 3. What is the significance of the Reynolds Number in practical applications?

The Reynolds Number is an important parameter in many fields, including aerodynamics, hydrodynamics, and heat transfer. It is used to predict the behavior of fluids in pipes, pumps, and other flow systems. It also helps engineers design more efficient and effective systems.

## 4. What is the drag constant in fluid dynamics?

The drag constant, also known as the drag coefficient, is a dimensionless quantity that represents the ratio of drag force to the product of fluid density, velocity, and frontal area. It is a measure of the resistance a fluid exerts on an object moving through it.

## 5. How is the drag constant affected by the Reynolds Number?

The drag constant is influenced by the Reynolds Number, as it is a function of the flow regime. At low Reynolds Numbers, the drag coefficient is relatively constant, while at high Reynolds Numbers, it decreases due to the transition from laminar to turbulent flow. This relationship is important in understanding the drag force experienced by objects in various flow conditions.