Unit 4 Flow Through Pipes, Fluid mechanics questions and answer

Unit 4 will acquaint you with the fascinating field of fluid mechanics by digging into the complexities of flow via pipes. Investigate major difficulties and solutions, and get a deeper understanding of the principles and equations governing fluid dynamics.

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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. Write examples of viscous flow and explain the characteristics of Laminar flow. 

Ans. A. Characteristics: 

• 1. There exists a shear stress in laminar flow, which is given by Newton’s law of viscosity, 

• 2. The laminar flow is rotational. 
• 3. There is a continuous dissipation of energy and for maintaining the flow we must supply the energy externally. 
• 4. Loss of energy (due to shear) ∝v.μ

Where,  v = velocity of flowing fluid, and

             μ =  viscosity of flowing fluid. 

• 5. No slip will occur at the boundary. 
• 6. There will be no mixing of layers occur. 
• 7. For laminar flow, Reynold’s number < 2000.

B. Examples of Laminar Flow: 

• 1. Movement of blood in veins and arteries of body. 
• 2. Rise of water in plants through their roots. 
• 3. Flow past tiny bodies.

Q2. Prove that the maximum velocity in a circular pipe for viscous flow is equal to two times the average velocity of flow.  

Ans. 

6. So, ratio of maximum velocity to average velocity will be equal to 2.

Q3. Prove that viscous flow through a circular pipe the kinetic energy correction factor equal to 2. 

Ans. 

Q4. What is turbulent flow ? Give its classification.  

Ans.

• 1. In a pipe, turbulent flow occurs when Re> 4000. 
• 2. Due to the fluid masses colliding with one another, a turbulent flow has erratic and chaotic fluid motion and total fluid mixing. 
• 3. Due to the differing velocities of the fluid masses in neighbouring layers, the exchange of fluid masses between the layers is followed by a transfer of momentum, which adds additional large magnitude shear stresses between adjacent layers.
• 4. Fluid viscosity has a negligible impact on total shear and is frequently disregarded. 
• 5. The turbulent motion can be classified as follows: 

i. Wall Turbulence: In boundary layer flows and in the near proximity of solid surfaces, where the fluid has a negligible mean acceleration, it happens. 

ii. Free Turbulence: It occurs in jets, wakes, mixing layers etc. 

iii. Convective Turbulence: It occurs where P.E. is changed into K.E. through the mixing process (eg., the turbulent flow in the annular space between the concentric rotating cylinders, conventional flow between parallel horizontal plates etc.). 

Q5. Describe this term: 

• A. Homogeneous Turbulence, 
• B. Isotropic Turbulence, 
• C. Turbulence Length scale; and 
• D. Turbulence intensity. 

Ans. A. Homogeneous Turbulence: 

• 1. Homogeneous turbulence is defined as having the same quantitative structure across the whole flow field.
• 2. The idea of homogenous turbulence suggests that the system’s velocity variations are arbitrary. The average turbulence properties are axis-invariant and independent of position inside the fluid. 
• 3.Consider the root mean square velocity fluctuations  

In homogeneous turbulence, the rms values of u’, v and w’ can all be different, but each value must be constant over the entire turbulent field.  

B. Isotropic Turbulence: 

• 1. If perfect disorder prevails and the statistical properties of the turbulence have no directional preference, the condition is known as isotropic. Its velocity variations are invariant to axis rotation and reflection because they are independent of the axis of reference.
•  2. In isotropic turbulence fluctuations are independent of the direction of reference and

C. Turbulence Length Scale: 

• 1. The magnitude of the enormous energy-containing eddies in a turbulent flow is described by the physical quantity known as the turbulence length scale, or I. 
• 2. A CFD simulation’s intake turbulent characteristics are frequently estimated using the turbulent length scale. 
• 3. Since this would suggest that the turbulent eddies are larger than the problem size, the turbulent length scale should typically not be larger than the problem dimension. 

D. Turbulence Intensity: 

• 1. Turbulence intensity is a scale characterizing turbulence expressed as a percent. 
• 2. A turbulence intensity rating of 0% corresponds to an idealized flow of air with zero variations in air speed or direction. On Earth, this idealized scenario is unheard of.
• 3. However, results higher than 100% are achievable due to the method used to calculate turbulence intensity. This may occur, for instance, when there are significant fluctuations and a low average air speed.

Q6. What are different methods of preventing the separation of boundary layers ? 

Ans. Methods of Preventing the Separation of Flow: 

i. Streamlined Body Shape:

1. The transition point of the boundary layer (from laminar to turbulent) can be pushed downstream using a streamlined body form, which lowers the skin friction drag. As a result, layer separation might be eliminated. 

ii. Acceleration of Fluid in the Boundary Layer: 

• 1. With this technique, we provide the fluid particles that are being slowed down in the boundary layer more energy. 
• 2. Energy can be transferred by 
  • a. Injecting the fluid into the region of boundary layer with the help of some device. 
  • b. through a slot in the body, a portion of the fluid is diverted from the high pressure region to the boundary layer’s retarded region.

iii. Motion of Solid Boundary : 

• 1. If we rotate a circular cylinder in a stream of fluid, the upper side of the cylinder will move in the same direction as the flow of fluid.
• 2. However, because the direction of fluid motion is the opposite of the motion of the cylinder, separation would take place on the lower side of the cylinder. 
  • iv. By sucking the retarded flow. 
  • v. By providing slots near the leading edge. 

vi. Energize the flow by introducing optimum amount of swirl in the incoming flow. 

vii. By suctioning through a porous surface, remove the fluid particles in the boundary layer that are retarded or travelling slowly.

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