Streamline Flow – Equation Of Continuity, Streamline vs Turbulent flow and their examples
Streamline flow is the flow in which all conditions at any point in a stream remain constant with respect to time.
Properties Of StreamLine Flow:
i) In streamline flow, liquid flow per second through any cross-sectional area is constant.
ii) Also in streamline flow, at every point, the velocity (both magnitude and direction) of every fluid particle passing through that point will be the same.
iii) In streamline flow the paths of two different particles will never intersect each other.
The path of any particle in a streamline flow is called a streamline. The direction of the velocity of any particle in a streamline is the tangent of the curve of the path.
No streamline intersects or mixes with each other in a streamline flow.
Here in the above figure, v1, v2, and v3 are the velocities of the streamline at points P, Q, and R respectively, and the directions of these velocities are tangential to the streamline.
Streamline Flow is a type of Streamflow. Streamflow is of two types:
i) Streamline Or Laminar Flow
ii) Turbulent Flow
In this article, we will discuss the first type that is Strwmline flow or Laminar Flow.
Equation Of Continuity Of Streamline flow:
Let there be fluid passing through a pipe with the streamlined flow.
Also Let, the velocity of the liquid be v1 at the lower end and v2 at the upper end and the area be A1 at the lower end and A2 at the upper end.
Now we consider a very small time interval Δt and let the fluid covers a distance of ΔX1 with velocity v1 at time interval Δt.
The volume of the fluid that will flow into the pipe through the lower end at time interval Δt will be:
V = A1X1
Also, we know that the mass (m) of an object is the product of density (ρ) x volume (V). So the mass of the fluid in the ΔX1 region will be:
Δm1 = Density x Volume
Δm1 = ρ1A1v1 Δt
Now will calculate the mass flux. Mass flux is the mass of fluid passed per unit of time through a cross-sectional area. So the mass flux for the lower end will be:
Mass flux ( Δm1/Δt) = ρ1A1v1 ……….. (1)
Similarly, the mass flux for the upper end will be:
Mass flux ( Δm2/Δt) = ρ2A2v2 ……….. (1)
As the flow is a steady flow, the density of the liquid in the lower end of the pipe and the upper end of the pipe will be the same.
Hence, the mass flux at the lower end of the pipe is equal to the mass flux at the upper end of the pipe.
=> ρ1A1v1 = ρ2A2v2 ……… (3)
This is the equation of continuity for a steady flow.
So we can say that mass flux throughout the pipe remains constant.
i.e ρ A v = constant
This is the equation of the law of conservation of mass in fluid dynamics.
If the fluid is compressible, the density will remain constant for steady flow.
Hence, ρ1 = ρ2
So the eq (3) will be written as:
A1v1 = A2v2 or Av = constant
Difference between Streamline Flow and Turbulent Flow:
i) In streamline flow, the fluid flows in parallel layers.
ii) The velocity of the liquid is low and steady.
iii) The velocity of the liquid is less than the critical velocity.
iv) The velocity of the fluid at a particular point in the streamline flow remains constant for every particle passing through that point.
v) The particles of streamline flow do not put pressure on the pipe inside which the liquid flows.
vi) There is no disruption or mixing of liquid layers.
i) In turbulent flow, the fluid does not flow in parallel layers.
ii) The velocity of the liquid is high and unsteady.
iii) The velocity of the liquid is higher than the critical velocity.
iv) The velocity of the fluid at a particular point in the turbulent flow changes for every particle passing through that point.
v) The particles of streamline flow puts pressure on the pipe inside which the liquid flows.
vi) Liquid layers disrupt and mix with each other.
Advantages Of Streamline Flow:-
i) The energy loss is very less in laminar flow.
ii) Streamline flow reduces energy consumption in pumping water using a pump.
iii) There is very little friction between the liquid layers.
Examples Of Streamline And Turbulent Flow:
Let’s take an example of water flowing from a tap. When the tap is open slightly the water from the tap flows smoothly and it will have a smooth texture, this is an example of streamlined flow.
After that if the flow rate is increased by further opening the tap, then there will be disturbances and voids after increasing the flow rate significantly, this is an example of turbulent flow.