Reynolds Number:
It is a dimensionless number which represents the ratio between inertial forces and viscous forces. Actually it tells us the relative effect of inertial forces and viscous forces acting on the moving fluid. Before further elaborating the idea of Reynolds number let us see that what are inertial force and viscous force?
Inertial Force:
It is the force exerted by any fluid by virtue of its state of motion. Suppose a fluid is moving at high velocity then, due to inertia, we are in need of a force to stop that moving fluid at an instant. More is the mass of fluid, more is the force needed to stop it. This is the force that is exactly equal to inertial force in magnitude but will not be the inertial force. So the force which backups or supports the flow of that corresponding fluid is known as inertial force. Here is another important point to note that as the force is given by the product of mass and acceleration, so if velocity of the moving fluid is constant than no inertial force acts on that fluid because acceleration in zero. It only depends upon the rate at which velocity is changing with respect to time.
Fig (1): fluid particles moving with constant velocity experience no inertial force.
Now let us see that what is viscous force?
Viscous Force:
It is the force which acts on the fluid due to the friction between the layers of the fluid. It can also be defined as the measure of the resistance to gradual deformation by shear stresses or tensile stresses. Actually these forces tend to nullify the relative movement of one layer of the fluid with respect to other layer due to friction between the layers. So we can deduce that more is the viscous force, less is the chance for the flow to become turbulent or chaotic.
Fig (2): Friction between layers of fluid restricts the relative movement of layers.
Now let us analyze that either Reynolds number has most important impact on incoming jet or not.
Reynolds number’s impact on incoming jet:
Before going into detail let us first see that about which incoming jet we are talking here.
A jet is actually an efflux of fluid that is restricted to move through a medium i.e. nozzle or orifice. A jet is also characterized as a high speed flow with a very little loss in regularity even after covering a considerable amount of distance. So we can say that the flow which is going to become jet is incoming jet. Now we discuss the impact of Reynolds number on incoming jet. When a simple flow is converted into jet a very large change in velocity occurs. This ‘large change’ increases the inertial forces within the fluid and hence the chance for the flow to become turbulent arises. But as we know that jet flow is very similar to streamline flow due to its ability to sustain its original shape, so it is unavoidable to deduce that viscous forces also increase at this instant to balance the inertial forces to keep the fluid streamline. After conversion from simple flow to jet flow inertial forces approach zero because now fluid velocity is not changing too rapidly. After all this discussion we infer that it is not the Reynolds number which influences the incoming jet but actually it is the fluid itself and the condition of boundary through which it is passing which decides a particular type of flow of fluid in that particular scenario. We can say that Reynolds number is not governing the flow of fluid. On the other hand Reynolds number is self-governed by the conditions of the flowing liquid.
Fig (3): jet flow of water
Keep in mind that Reynolds number can be used as a criterion to decide that, at a particular value of acceleration, whether the flow is turbulent or streamline. For example, low value of Reynolds number indicates that the corresponding flow is dominated by viscous force which results in streamline flow. On the other hand if the value of Reynolds number is sufficiently large then the corresponding flow is dominated by inertial force which results in turbulent flow. So understanding this predicting capability of Reynolds number we may conclude that Reynolds number influences the incoming jet of a fluid.
Fig (4): Schematic of turbulent and laminar flow
Can Reynolds number be changed in any design compatible to orifice parameters?
Actually orifice is any opening through which something may pass. So that opening must have some particular geometric shape i.e. circular or rectangular. If it is circular, then the diameter of the orifice opening is an important design parameter. Also length plays important role as a design parameter. If the diameter of orifice is very small, then fluid passing through it must attain high magnitude of speed according to equation of continuity. This sudden increase in speed, increase the inertial forces within the fluid so that flow becomes turbulent. As Reynolds number is directly proportional to inertial force so the magnitude of Reynolds number also increases. We may prefer to select the Reynolds number as flow predicting criteria for the flow of corresponding liquid. So the Reynolds number impels us to choose appropriate dimensions for the orifice opening because just speed is not important. For example, in case of water turbine you may prefer a mechanism which produces high speed water jets to rotate the turbine blades but at the same time the prevalence of turbulence on fluid flow forces you to choose appropriate speeds to keep the flow streamline to avoid the phenomenon like back pressure etc... But if you want high speeds then you must decrease the density of that fluid or decrease the characteristic length of orifice or increase the viscosity of the fluid by proper amount. Decreasing the density is often practically impossible; also it is hard to change the viscosity of a fluid under specific conditions. The only thing which we can use to handle the flow is the diameter and characteristic length of orifice. By making a smart combination of orifice parameters with speed, viscosity and density of fluid we can achieve our goal.
Fig (5): flow of fluid through the opening of orifice
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