Type of Flow MCQ Quiz in मल्याळम - Objective Question with Answer for Type of Flow - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Concept:

Streamline is a line everywhere tangent to the velocity vector at a given instant

Path line is the actual path traversed by a given fluid particle.

The streak line is the locus of particles that have earlier passed through a prescribed point.

For steady flow, streamlines, pathlines, and streak lines are identical because:

• For a steady flow, the velocity vector at any point is invariant with time.
• The path line of the particles with different identities passing through a point will not differ.
• The path line could coincide with one another in a single curve which will indicate the streak line too.

Explanation:

An unsteady Flow is defined as a flow in which the hydrodynamic parameters and fluid properties change with time. When the velocity and other hydrodynamic parameters changes from one point to another the flow is defined as non-uniform.

The opening of a valve in pipeline changes fluid properties with time, hence it is unsteady flow.

Explanation:

1. A streamline is a line everywhere tangent to the velocity vector at a given instant.
2. A pathline is the actual path traversed by a given fluid particle.
3. A streakline is the locus of particles that have earlier passed through a
prescribed point.
4. A timeline is a set of fluid particles that form a line at a given instant.

Additional Information

Streamlines, pathlines, and streaklines are identical in a steady flow. 

Concept:

\(\bar v = 3\hat i + 5\hat j\)

u = 3, V = 5

Equation of streamline

\(\frac{{dx}}{u} = \frac{{dy}}{v}\)

\(\frac{{dx}}{3} = \frac{{dy}}{5}\)

∴ 5 dx – 3 dy = 0

Explanation:

For a velocity Vector \(\;\vec V = u\hat i + v\hat j + w\hat k\)

where u, v, and w are velocity components along x, y and z-direction respectively

Then its acceleration

Along x-direction \({a_x} = u\frac{{\partial u}}{{\partial x}} + \;v\frac{{\partial u}}{{\partial y}} + w\frac{{\partial u}}{{\partial z}} + \frac{{\partial u}}{{\partial t}}\;\)

Along y-direction \({a_y} = u\frac{{\partial v}}{{\partial x}} + \;v\frac{{\partial v}}{{\partial y}} + w\frac{{\partial v}}{{\partial z}} + \frac{{\partial v}}{{\partial t}}\;\)

Along z-direction \({a_z} = u\frac{{\partial w}}{{\partial x}} + \;v\frac{{\partial w}}{{\partial y}} + w\frac{{\partial w}}{{\partial z}} + \frac{{\partial w}}{{\partial t}}\;\)

Then the magnitude of total acceleration \(a = \sqrt {a_x^2 + a_y^2 + a_z^2\;} \)

There are two components of the acceleration

• \(u\frac{{\partial u}}{{\partial x}} + \;v\frac{{\partial u}}{{\partial y}} + w\frac{{\partial u}}{{\partial z}}\;\) this group is called convective acceleration and
• \(\frac{{\partial u}}{{\partial t}}\) this group is called temporal acceleration.

Types of Accelerations for Different Types of Streamlines Patterns for steady flow.

Concept-

Uniform flow-

• Uniform flow is the type of fluid flow in which the velocity of the flow at any given time does not change with respect to space.

Non uniform flow-

• A non-uniform flow is a type of fluid flow in which the velocity of the flow at any given time changes with respect to space. 

Steady Flow-

• A flow is defined steady when its fluid characteristics like velocity, density, and pressure at a point do not change with time.

Unsteady flow-

• A flow is defined unsteady, when the fluid characteristics velocity, pressure and density at a point changes with respect to time.  

Given, \(\vec V = ax\hat i + ay\hat j\)

i.e. u_x = ax and u_y = ay

Equation of stream line is given by

\(\begin{array}{l} \frac{{dx}}{{{u_x}}} = \frac{{dy}}{{{u_y}}}\\ \Rightarrow \frac{{dx}}{{ax}} = \frac{{dy}}{{ay}}\\ \Rightarrow \frac{{dx}}{x} = \frac{{dy}}{y} \end{array}\)

Inx = Iny + Inc

∴ x = c y

Since the stream line passes through point (1, 2), therefore

1 = 2c ⇒ c = ½

x = ½ y

⇒ 2x – y = 0

Explanation: 

Laminar flow: Laminar flow occurs when the fluid flows in infinitesimal parallel layers with no disruption between them. In laminar flows, fluid layers slide in parallel, with no eddies, swirls, or currents normal to the flow itself. 

Compressible flow: In this type of flow density of fluid does not remain constant during the flow, it may change according to flow.

Uniform flow: If the velocity vector at all the points in the flow is the same at any instant of time then the flow is uniform flow.

Unsteady flow: If the fluid and flow characteristics at a point may change with time, then the flow is unsteady. 

Explanation:

Laminar flow:

• Laminar flow occurs when the fluid flows in infinitesimal parallel layers with no disruption between them as shown in Fig. (a)
• In laminar flows, fluid layers slide in parallel, with no eddies, swirls, or currents normal to the flow itself.
• This type of flow is also referred to as streamline flow because it is characterized by non-crossing streamlines.

Turbulent flow: 

• In a closed pipe, when fluid layers slide is not in parallel to the other layer, then the flow is called turbulent flow. Fig. (b)

a) 

b) 

Important Points

Reynolds number:

The Reynolds number is an important dimensionless quantity in fluid mechanics used to predict flow patterns in different fluid flow situations.

• Reynolds number is below 2000, laminar flow happens.
• Reynolds number is above approximately 4000, the flow will be turbulent.
• In between these two limits, the flow is termed as “transition flow”.

Concept:

\(\frac{D}{Dt}=\frac{\partial}{\partial t}+u\frac{\partial}{\partial x}+v\frac{\partial}{\partial y}+w\frac{\partial}{\partial z}\)

The total differential D/Dt is known as the material or substantial derivative with respect to time.

The first term ∂/∂t in the right-hand side of is known as a temporal or local derivative which expresses the rate of change with time, at a fixed position. The last three terms in the right-hand side of are together known as a convective derivative which represents the time rate of change due to change in position in the field.

So total acceleration can be zero.