Fluids… The basic term in all of the concept of fluid dynamics and the basis behind the concept of flows. But what exactly is a fluid..?
A fluid is a substance that continuously deforms (flows) under an applied shear stress or external force in physics. Fluids are a type of matter that comprises of liquids, gases, and plasmas. They are substances with zero shear modulus, or, to look at it in a more simpler or another way, substances that cannot endure any shear force applied to them.
Now that we know what exactly fluids are.. lets consider the term fluid flow. So, in broad sense, fluid flow is a branch of fluid mechanics that deals with fluid dynamics. It is typified by the motion of a fluid subjected to unbalanced forces. This motion would then continue indefinitely as long as unbalanced forces are applied.
Consider the following graph
Ideal fluid
When a fluid cannot be compressed and its viscosity does not fit into the category of an ideal fluid, it is said to be ideal. It is a fictitious fluid that does not exist in reality.
Real fluid
All the fluids are real as all the fluid possess viscosity.
Newtonian fluid
A fluid is said to be Newtonian if it obeys Newton’s law of viscosity.
Non-Newtonian fluid
When the fluid doesn’t obey Newton’s law of viscosity, it is known as Non-Newtonian fluid.
Ideal plastic fluid
It is known as ideal plastic fluid when the shear stress is proportional to the velocity gradient and the shear stress is greater than the yield value.
Incompressible fluid
When the density of the fluid doesn’t change with the application of external force, it is known as an incompressible fluid.
Compressible fluid
Compressible fluid is characterized as fluid whose density changes in response to variations of external force.
Now that we’ve seen the numerous different types of fluids… Let us now look at the various types of flows.
There are three types of fluid flows, which are as follows:
Flow Laminar
Flow in Turbulence
Flow of Vortices
Illustration 1: A Simple Visual to Demonstrate the Various Flow Types
The flow differential equations have two solutions: time-independent and time-dependent. In the first case, the fluid velocity at each point is constant in time, and the resulting flow is alluded to as laminar. The flow is turbulent if the velocity changes over time.
The shape of the surface of a cylindrical water beam, smooth for laminar flow or rough for turbulent flow, is used to conceptualize flow. The roughness tends to increase as the turbulence increases, as measured by the Reynolds number. To calculate the integral, the volume flow rate through a surface S is calculated knowing the velocity of the fluid at each point of the surface:
When the velocity over the surface S is constant, this equation is simple to integrate. However, maintaining a constant velocity on a surface is difficult. Instead, we can measure the flow in the tube and divide the result by the area of the tube to get the average velocity of the water. To compensate for the movement of a cylindrical segment of water inside a hose, a pressure difference between its ends must be applied.
The water velocity is zero next to the tube wall and maximum at its center in laminar flows, a result obtained by envisioning a cylinder of water interacting with pressure applied to its ends.
Reynolds Number and its Significance in Determining The Flow Types
The Reynolds Number is a significant feature that helps determine whether a flow is laminar, turbulent, or vorticial.
Remember that the Reynolds Number is purely and simply a mathematical term which can be used to determine the flow type and is a dimensionless quantity.
If its value is less than 2300 the flow is laminar and if greater than 4000 the flow is turbulent (in cylindrical pipes). Between 2300 and 4000 it is considered a transition regime.
Turbulence is the most important unsolved problem of classical physics.
- Richard Feynman -
Laminar Turbulent And Vortex Flow
Laminar Flow
Laminar flow is a type of fluid flow (gas or liquid) in which the fluid travels in smooth or regular paths. The velocity, pressure, and other flow properties at each point in the fluid remain constant in laminar flow, also recognized as streamline flow. Laminar flow over a horizontal surface could be described as a series of parallel thin layers, or laminae.
Laminar flow in a straight pipe can be visualized of as the relative motion of a series of concentric cylinders of fluid, the outside one fixed to the pipe wall and the others moving at increasing speeds as the pipe’s center approaches. Laminar flow occurs when smoke rises in a straight path from a cigarette. After a short distance, the smoke usually morphs into a turbulent flow, as it eddies and swirls from its regular path.
Properties of laminar flow:
- Re < 2000
- ‘low’ velocity
- Fluid particles move in straight lines
- Layers of water flow over one another at different speeds with virtually no mixing between layers.
- The flow velocity profile for laminar flow in circular pipes is parabolic in shape, with a maximum flow in the center of the pipe and a minimum flow at the pipe walls.
- The average flow velocity is approximately one half of the maximum velocity.
- Simple mathematical analysis is possible.
- Rare in practice in water systems.
Laminar flow examples:
- The blood in your body flows in a laminar pattern.
Syrup or honey is dripping from the nozzle. The Reynolds number means that the flow is very laminar since the liquid is so dense or viscous.
Turbulent Flow
Turbulent flow is a type of fluid (gas or liquid) flow in which the fluid ebbs and flows or mixes irregularly, as contrasted to laminar flow, in which the fluid moves in smooth paths or layers. In turbulent flow, the speed of the fluid at a given point is continually evolving in magnitude and direction.
Even if the currents are gentle, the flow of wind and rivers is generally turbulent in this sense. The air or water swirls and eddies while the bulk of it moves in a specific direction.
Properties of Turbulent flow:
- Re > 4000
- high’ velocity
- The flow is characterized by the irregular movement of particles of the fluid.
- Average motion is in the direction of the flow
- The flow velocity profile for turbulent flow is fairly flat across the center section of a pipe and drops rapidly extremely close to the walls.
- The average flow velocity is approximately equal to the velocity at the center of the pipe.
- Mathematical analysis is very difficult.
- Most common type of flow.
Examples of Turbulent flow:
- Blood flow in lungs, oil transport in pipelines, lava flow, the atmosphere, and ocean waves, Flow in pumps and engines, as well as flow in boat wakes and around aircraft wing tips are all examples of turbulent flow.
Vortex Flow
A vortex is a region in a fluid at which flow revolves around an axis line, which can be straight or curved. Vortices form in stirred fluids that can be seen in smoke rings, whirlpools in the wake of a boat, and the winds surrounding a tropical cyclone, tornado, or dust devil.
In the absence of external forces, viscous friction within the fluid tends to organize the flow into a collection of irrotational vortices, that may be superimposed on larger-scale flows, including larger-scale vortices. Vortices, once formed, can move, stretch, twist, and interact in a number of ways. A moving vortex carries angular and linear momentum, energy, and mass with it.
What is a vortex flow, and how does it work? When a liquid-filled cylindrical vessel is rotated around its vertical axis, the liquid surface is depressed at the axis of rotation and rises near the vessel’s walls on all sides.
Vortex flow is the name for this kind of flow. It is divided into two types:
1. Forced vortex flow: In this form of flow, an external torque is used to cause the liquid-filled vessel to rotate around a fixed vertical axis.
2. Free vortex flow: In this form of flow, liquid particles follow circular paths around a fixed vertical axis without any external torque. Free vortex flow can be seen in the flow of water through the hole in the bottom of a wash basin.
The following relevant points about vortex flow should be noted:
(a) The surface of a liquid in a cylindrical vessel assumes the form of a paraboloid as it is revolved.
(b) The depression of liquid at the axis of rotation is the same as the rise of liquid along the walls of a spinning cylinder around the initial level.
© The average pressure on the bottom of a closed cylindrical vessel fully filled with a liquid equals the total centrifugal pressure plus the weight of the liquid in the vessel.
(d)The total pressure (P) on the top of a closed cylindrical vessel of radius (r) fully filled with a liquid of particular weight (w) and rotating around its vertical axis is calculated as follows:
P=π w ω² r² / 4g
(e) The water factor with a free vortex has a tangential velocity (v) that is inversely proportional to its distance from the center.
Conclusion
Visual graphics are more effective at explaining a topic. The descriptive pictures tend to simplify the important concept of fluid flow. The significance of the concept of Reynolds Number, which aids in the determination of flow types, is also emphasized.
I would like to thank my group members Shrutish Gadakh, Sanket Dhut, Shrushti Fuley and Dhruv Bansal for their immense contribution in developing a simple way to generate this blog for the understanding of each and every one, in a simple, yet descriptive manner.
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