Unit 2 TYPES OF FLUID in Fluid Mechanics AKTU Btech Important Question

Unit 2 of Fluid Mechanics Ideal and real fluids, Newtonian and non-Newtonian fluids, compressible and incompressible fluids, and other fluid types are covered by AKTU Btech. The essential questions in this unit include the properties and characteristics of many types of fluids, their behavior in various conditions, and their relevance in several fields. Understanding this topic is crucial for students to grasp the fundamentals of fluid mechanics and use it to solve challenging problems.

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Important Questions For Fluid Mechanics:
*Unit-01     *Unit-02    
*Unit-03    *Unit-04 
*Unit-05    *Short-Q/Ans
*Question-Paper with solution 21-22 

Q1. Explain the following with example: 

• a. Steady and unsteady flows, 
• b. Laminar and turbulent flows,
• c. Rotational and irrotational flows, 
• d. Compressible and incompressible flows, and Uniform and non-uniform flows. 

Ans. a. Steady and Unsteady Flows: 

1. Steady Flow is defined as that type of flow in which the fluid characteristics like velocity, pressure, density, ete., at a point do not change with time. Mathematically, 

Example: Flow of liquid through a long pipe of constant diameter at a constant rate. 

2. Unsteady flow is that type of flow, in which the velocity, pressure density at a point changes with respect to time. Mathematically, 

Example: Flow of liquid through a long pipe of constant diameter at either increasing or decreasing rate. 

b. Laminar and Turbulent Flows: 

1. Laminar flow is described as those flow types where all of the stream-lines are straight and parallel and the fluid particles move along well defined routes or stream-lines. 

Example: Flow through a capillary tube. 

• 2. When there is turbulent flow, the particles travel in a zigzag pattern.Example: Flow in natural streams, artificial channels, sewers etc. 
• 3. The flow is referred to as laminar if the Reynold number is less than 2000. It is referred to as turbulent flow if the Reynold number is more than 4000. When there is turbulent flow, the particles travel in a zigzag pattern. 

c. Rotational and Irrotational Flows: 

1. Rotational flow is a type of flow in which the fluid particles spin about their own axes while still moving along stream lines. 

Example: Flow of liquid in the rotating tanks. 

2. Irrotational flow is a term used to describe a flow in which the fluid particles do not rotate about their own axis while moving along stream lines. 

Example: Flow over a drain hole of a stationary tank or a wash basin.

d. Compressible and Incompressible Flows: 

1. Compressible flow is that type of flow in which the density of the fluid changes from point to point, or in other words the density (p) is not constant for the fluid. Mathematically,   

Examples: Flow of gases through orifices nozzles, gas turbines etc. 

2. Incompressible flow is that type of flow in which the density is constant for the fluid flow. Mathematically, 

Examples: Subsonic aerodynamics. 

e. Uniform and Non-uniform Flows: 

1. Uniform flow is characterised as a type of flow in which the velocity with regard to space is constant over time. Mathematically, 

Example: Flow through a straight pipe of constant diameter. 

2. The type of flow known as non-uniform flow occurs when the velocity fluctuates over time in relation to space. Mathematically, 

Example: Flow around a uniform diameter pipe-bend or a canal bend and flow through a non-prismatic pipe or channel.

Q2. Streamlines, path lines and streak lines are identical for steady flow. Explain. 

Ans.

• 1. A path line is the path or trajectory traced out by a moving fluid particle. 
• 2. This method could be applied to research the path a pollutant takes when it leaves a smoke stack.
• 3. Sometimes, we could decide to fix our gaze on a certain place in space and count every fluid particle that passes through it using dye or smoke.
• 4. After a short while, the flow would contain a number of distinguishable fluid particles that had all once passed through a single fixed point in the space.
• 5. The line joining these fluid particles is defined as a streak line. 
• 6. Streamlines are lines that are drawn in the flow field so that they are always perpendicular to the flow direction at all points. 
• 7. The streamline shape does not change from one instant to the next in a steady flow because the velocity at each point in the flow field is constant over time. This suggests that a particle that happens to be on a certain streamline will always follow that streamline.
• 8. Additionally, if two particles pass through the same fixed point in space at the same time, they will be on the same streamline and will stay there. As a result, in the flow field of a steady flow, path lines, streak lines, and stream lines are all the same lines.

Q3. Write short note on :

• A. Subsonic, sonic and supersonic flows. 
• B. Subcritical, critical and supercritical flows. 
• C. One, two and three dimensional flows  

Ans. A. Subsonic, Sonic and Supersonic flow : 

• 1. Mach number is a dimensionless number that serves as the basis for the definitions of subsonic, sonic, and supersonic flow.
• 2 When Mach number is less than 1 (M< 1), flow is to be called subsonic flow. 
• 3. When Mach number is equal to 1 (M= 1), flow is to be called sonic flow. 
• 4. When Mach number is greater than 1 (M > 1), flow is to be called supersonic flow.  

B. Subcritical, Critical and Supercritical flow: 

• 1. When Froude number is less than one (Fe < 1 flow. the flow is subcritical 
• 2. When Froude number is equal to one (Fe = 1), the flow is critical flow. 
• 3. When Froude number is greater than one (Fe> 1), the flow is supercritical flow. 

C. One, Two and Three Dimensional flow: 

• 1. One dimensional flow is that type of flow in which the flow parameter such as velocity is a function of time and one space coordinate only. Mathematically,   u= f(x), v = 0 and w =0. 
• Where u, v and w are velocity components in a, y and z directions respectively.
• 2. Two-dimensional flow is that type of flow in which the velocity is a function of time and two rectangular space coordinates. Mathematically,     u = f₁(x, y), v =f₂(x, y) and w = 0
• 3. Three-dimensional flow is that type of flow in which the velocity is a function of time and three mutually perpendicular directions. Mathematically,  u =f₁(x, y, z), V =f₂(x, y, z) and w =f₃(x, y, z)

Q4. What is the difference between Eulerian and Lagrangian approach ?

Ans. Difference between the Lagrangian and Eulerian Methods: 

Q5. Write a short note on circulation.  

Ans. 1. Let us consider a closed curve in a two-dimensional flow field as shown in Fig., the curve being cut by the streamlines. 

2. Let P be the point of intersection of the curve with one streamline, 0 be the angle which the streamline makes with the curve. 

3. The component of velocity along the closed curve at the point of intersection is equal V cos θ.

4.. Circulation Г is defined mathematically as the line integral of the tangential velocity about a closed path (contour). 

Where,               V= Velocity in the flow field at the element ds, and

                          θ = Angle between V and tangent to the path (in the positive anticlockwise                                    direction along the path) at the point.

Q6. What is the relationship between equipotential line and line of constant stream function at the point of intersection?

Ans. 

4. The product of the slope of the equipotential line and the stream of the slope of the point of intersection is equal to -1.

5. Thus the equipotential lines are orthogonal to the points of intersection.

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