What is the Reynolds number for a sphere in laminar flow?
Note that purely laminar flow only exists up to Re = 10 under this definition. Under the condition of low Re, the relationship between force and speed of motion is given by Stokes’ law. At higher Reynolds numbers the drag on a sphere depends on surface roughness.
How do you find the Reynolds number for a sphere?
The most widely studied case is the sphere. Figure 1 graphs the dependence of drag coefficient for a sphere and a cylinder in crossflow on the Reynolds Number Re = ρuD/η, where D is the sphere (cylinder) diameter, η the viscosity of liquid, and .
What is the critical Reynolds number for a sphere?
The drag coefficient of a sphere will change rapidly from about 0.5 to 0.2 at a Reynolds number in the range of 300000.
What is the effect of fluid flow over sphere?
The flow lines are straight and uniform in the free stream far in front of the sphere, but they are deflected as they pass around the sphere. For a large distance away from the sphere the flow lines become somewhat more widely spaced, indicating that the fluid velocity is less than the free-stream velocity.
How is flow described using the Reynolds number?
The Reynolds number, referred to as Re, is used to determine whether the fluid flow is laminar or turbulent. Technically speaking, the Reynolds number is the ratio of the inertial forces to the viscous forces. This ratio helps to categorize laminar flows from the turbulent ones.
How do you know if a flow is turbulent or laminar?
For practical purposes, if the Reynolds number is less than 2000, the flow is laminar. If it is greater than 3500, the flow is turbulent. Flows with Reynolds numbers between 2000 and 3500 are sometimes referred to as transitional flows.
How does Reynolds number effect flow separation?
As the Reynolds number increases, flow separation gradually develops, and this corresponds to a change from a regime of flow dominated by viscous effects, with viscous forces and pressure forces about equally important, to a regime of flow dominated by flow-separation effects, with pressure forces far larger than …
What happens when the Reynolds number equals the critical Reynolds number?
The critical Reynolds number is associated with the laminar-turbulent transition, in which a laminar flow becomes turbulent. For flow over a flat plate, transition from laminar to turbulent boundary layer occurs when Reynolds number at x exceeds Rex,crit ~ 500,000. …
What is the nature of Stokes force?
In Stokes’s law, the drag force F acting upward in resistance to the fall is equal to 6πrηv, in which r is the radius of the sphere, η is the viscosity of the liquid, and v is the velocity of fall. …
How do you calculate Reynolds number?
The Reynolds number (Re) of a flowing fluid is calculated by multiplying the fluid velocity by the internal pipe diameter (to obtain the inertia force of the fluid) and then dividing the result by the kinematic viscosity (viscous force per unit length).
How are flows characterized by the Reynolds number?
Keep in mind that they are characterized or described completely by the Reynolds number, and only by the Reynolds number: it is not just the size of the sphere, or the velocity of flow around it, or the kind of fluid; it is how all of these combine to give a particular value of the Reynolds number.
Is there a relationship between drag coefficient and Reynolds number?
So far we have considered flow past a sphere only from the standpoint of dimensional analysis, in Chapter 2, to derive a relationship between drag coefficient and Reynolds number, and we have looked at flow patterns and fluid forces only at very low Reynolds numbers, in the Stokes range.
How are high Reynolds numbers different from low Reynolds numbers?
At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers turbulence results from differences in the fluid’s speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow (eddy currents).
How is the Reynolds number used to calculate the fall velocity?
The particle Reynolds number is important in determining the fall velocity of a particle. When the particle Reynolds number indicates laminar flow, Stokes’ law can be used to calculate its fall velocity. When the particle Reynolds number indicates turbulent flow, a turbulent drag law must be constructed to model the appropriate settling velocity.