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Q.1 : Equation of continuity is based on____________
Ans. Law of conservation of mass
Q.2 : What does equation of continuity describe?
Ans. It describes that the rate at which mass leaves the system is equal to the rate at which mass enters a system.
Q.3 : What is streamlined flow?
Ans. In steady flow, the pattern of streamlines is stationary
Streamline Flow In Physics, Types Of Flow, Equation Of Continuity, Important Topics JEE 2025
Streamline flow in physics : Streamline flow in physics describes the smooth, uninterrupted movement of a fluid, where velocity and pressure remain constant along imaginary paths called streamlines. This phenomenon is fundamental in understanding fluid dynamics and has applications in various fields, from aerodynamics to hydrodynamics.
Shrivastav 13 May, 2024
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Streamline Flow In Physics :
In This Article We will learn that in steady flow the velocity of fluid particles reaching a particular point is the same at all time. Thus, each particle follows the same path as taken by a previous particle passing through that point. If the liquid is pushed in the tube at a rapid rate, the flow may become turbulent. In this case, the velocities of different particles passing through the same point may be different and change erratically with time. The motion of water in a high fall or a fast-flowing river is, in general, turbulent. Steady flow is also called
streamline flow
.
Streamline Flow In Physics
Ideal Fluid:
An incompressible, streamline, irrotational, non-viscous fluid is called an
ideal fluid (SIIN fluid)
. So, an ideal fluid (i.e. a Steady, Irrotational, Incompressible and Non viscous liquid is an SIIN fluid.
Steady Flow:
If the fluid velocity at any point is constant in time, then the flow is said to be
steady
.
Non-Steady Flow:
If the fluid velocity at any point varies with time, then the flow is said to be
non-steady
.
Streamline:
A
streamline
is a curve, the tangent to which at a point gives the direction of fluid velocity at that point.
It is analogous to a line of force in an electric or magnetic field.
Pattern Of Streamline Flow In Physics
Pattern Of Streamline Flow In Physics :
In steady flow, the pattern of streamlines is stationary with time and therefore, also called a
streamline
flow.
No two streamlines can ever cross one another, for if they did, a fluid particle arriving at that point would have possessed two directions (or two velocities) and hence the flow would never be steady.
In order to simplify the discussion, we make several assumptions:
(i)
The flow is steady:
The velocity and pressure at each point are constant in time
(ii)
The fluid is incompressible:
The density of fluid is constant throughout.
(iii)
The flow is irrotational:
A tiny paddle wheel placed in the liquid will not rotate. In rotational flow, for example, in eddies, the fluid has net angular momentum about a given point.
(iv)
The fluid is non viscous:
There is no dissipation of energy due to internal friction between adjacent layer in the fluid.
Types Of Streamline Flow In Physics
Types Of Streamline Flow :
In physics, streamline flow can be categorized into two main types: laminar flow and turbulent flow. Laminar flow occurs when a fluid flows in parallel layers with minimal mixing between them, resulting in smooth and predictable motion. This type of flow is characterized by orderly streamlines and is often observed in low-viscosity fluids moving at low velocities. In contrast, turbulent flow involves chaotic and unpredictable movement, with irregularly shaped streamlines and mixing between adjacent fluid layers. It occurs at higher velocities or in fluids with higher viscosity and is commonly found in natural phenomena like rivers or in engineering applications like pipe flow.
Streamline Flow : Tube Of Flow
A tubular region of fluid enclosed in by a boundary consisting of streamlines is called a
tube of flow
.
No fluid can cross the boundaries of a tube of flow and, therefore, a tube of flow behaves like a pipe of the same shape.
Rotational Flow :
The flow of liquid is said to be
rotational
if the angular velocity is non zero.
Irrotational Flow :
The flow of the fluid is said to be
irrotational
if the element of the fluid at each point has no net angular velocity.
Streamline Flow : Line of Flow
The path taken by a particle in flowing fluid is called its line of flow. The tangent at any point on the
line of flow
gives the direction of motion of that particle at that point. In the case of steady flow, all the particles passing through a given point follow the same path and hence we have a unique line of flow passing through a given point. In this case, the line of flow is also called a
streamline
. Thus, the tangent to the streamline at any point gives the direction of all the particles passing through that point. It is clear that two streamlines cannot intersect, otherwise, the particle reaching at the intersection will have two different directions of motion.
Consider an area
S
in a fluid in steady flow. Draw streamlines from all the points of the periphery of
S
. These streamlines enclose a tube, of which
S
is a cross section. Such a tube is called a tube of flow. As the streamlines do not cross each other, fluid flowing through different tubes of flow cannot intermix, although there is no physical partition between the tubes. When a liquid is passed slowly through a pipe, the pipe itself is one tube of flow.
It is the most common graphical concept of flow visualization. It is a line drawn such that a tangent at every point of it is in the direction of velocity at that instant.
A collection of streamlines drawn in this manner represents the complete flow pattern at an instant. Thus, for an unsteady flow, the streamline pattern may or may not remain the same at the next instant. Note that if the unsteadiness is due to a change in the magnitude of the velocity, then the streamline pattern still remains the same at different instants of time. On the other hand, if the unsteadiness is due to change in the direction of the velocity, the pattern will change from time to time.
Unlike path lines, a streamline cannot intersect itself; furthermore, two streamlines cannot meet or intersect at a point. This is because instantaneously fluid can have a unique velocity at a point.
Streamline Flow
If every point of a steadily flowing liquid follows exactly the same path that has been followed by the particles preceding it, the flow is said to be streamlined. The path is known as ‘streamline’. In Fig. the paths 1, 2, 3 are streamlines. If a liquid follows the path
ABC
, particles following it move along the same path.
Streamline Flow : Turbulent flow
When the velocity exceeds a certain critical value, the nature of flow becomes complicated. Random, irregular, local currents (called vortices) develop throughout the fluids. The resistance to the flow increases tremendously. This type of flow is called 'turbulent flow'.
Equation Of Continuity
Equation Of Continuity :
Consider a steady, irrotational flow of an ideal fluid through a tube of varying cross-section having no source or sink between the entry and the exit. If,
A
1
and
A
2
are the cross-sectional areas at points 1 and 2 respectively,
v
1
and
v
2
are the respective velocities of the liquid entering at 1 and leaving at 2 as shown in Figure.
If
is the mass of liquid entering per second, then we have
As there is no source and sink between the entry and the exit, so we have
This is called the Equation of Continuity and follows from the Law of Conservation of Mass to the flow of the ideal fluids.
Equation of Continuity Flow
Equation of Continuity Flow :
The quantity
is called the flow rate or volume flux or volume of liquid flowing per second and is also denoted by
Q
.
(a)
Velocity flux is the measure of the volume of liquid flowing in or out per second for a surface, the surface held normally to the liquid velocity (or liquid flow).
(b)
The more the value of velocity flux, the more the number of streamlines cross the surface.
(c)
We may also interpret the streamline picture as follows. In a narrow part of the tube the streamlines get closer together than in a wide part. Thus, as the distance between the streamlines decreases, the speed of the fluid increases.
(d)
Widely spaced streamlines indicate regions of low speed, whereas closely spaced streamlines indicate regions of high speed.
(e)
In hilly region, where the river is narrow and shallow (i.e., small cross-section) the water current will be faster, while in plains where the river is wide and deep (i.e., large cross-section) the current will be slower, and so deep water will appear to be still.
(f)
When water falls from a tap, the velocity of falling water under the action of gravity will increase with distance from the tap. So, in accordance with continuity equation the cross section of the water stream will decrease and due to which the falling stream of water becomes narrower.
Consider two such points on the water stream having a separation
h
, areas
A
1
,
A
2
and respective velocities
v
1
and
v
2
, then from Equation of Continuity, we have
A
1
v
1
=
A
2
v
2
Now, since we have
(
A
2
<
A
1
)
(i)
If liquid entering a tube leaves the tube at two other points, and assuming that the tube has no source and sink, then we have
a
1
v
1
=
a
2
v
2
+
a
3
v
3
Streamline Flow Illustration 1
Water is flowing in a circular pipe of varying cross-sectional area, and at all points the water completely fills the pipe.
(a)
At one point in the pipe the radius is 0.2 m. What is the magnitude of the water velocity at this point if the volume flow rate in the pipe is 1.20 m
3
s
–1
?
(b)
At a second point in the pipe the water velocity has a magnitude of 3.80 ms
–1
. What is the radius of the pipe at this point?
Solution:
(a)
Q
= volume flow rate =
Av
(b)
From continuity equation
A
1
v
1
=
A
2
v
2
r
2
= 0.317 m
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