All questions of Fluid Mechanics for Mechanical Engineering Exam

Understanding the Reynolds Number
The Reynolds number (Re) is a dimensionless quantity used to predict flow patterns in different fluid flow situations. It is defined as the ratio of inertial forces to viscous forces in a fluid. The formula for calculating the Reynolds number is:
Re = (Density × Velocity × Characteristic Length) / Viscosity
This number helps in determining whether the flow is laminar, transitional, or turbulent.
Flow Regimes Based on Reynolds Number
- Laminar Flow:
- Occurs when Re < />
- Fluid flows in parallel layers with minimal disruption between them.
- Transitional Flow:
- Occurs when Re is between 2000 and 4000
- Flow is unstable and can switch between laminar and turbulent.
- Turbulent Flow:
- Occurs when Re > 4000
- Characterized by chaotic property changes, such as velocity and pressure fluctuations.
Why Re > 4000 Indicates Turbulent Flow
- Inertial Forces Dominate:
- In turbulent flow, the inertial forces are significantly greater than viscous forces, leading to irregular and swirling motions.
- Mixing and Energy Dissipation:
- Turbulent flow enhances mixing and energy dissipation, making it suitable for many engineering applications, such as in piping systems.
- Practical Implications:
- Engineers must identify turbulent flow for proper design and analysis of systems to ensure efficiency and safety.
In conclusion, the flow in a pipe is considered turbulent when the Reynolds number is greater than 4000. Understanding this concept is crucial in mechanical engineering for designing efficient fluid transport systems.

Bluff Body and Pressure Drag

Bluff Body: A bluff body is a three-dimensional object that has a blunt shape and has a high drag coefficient. Examples of bluff bodies are cylinders, spheres, cubes, and other shapes that have a large cross-sectional area perpendicular to the flow direction.

Pressure Drag: Pressure drag is the force that opposes the motion of a body through a fluid due to the pressure difference between the front and rear of the body. It is caused by the separation of the fluid flow from the surface of the body, resulting in a low-pressure region behind the body.

Explanation

Bluff bodies have a high drag coefficient because they create a large wake behind them, which creates a low-pressure region. The pressure difference between the front and rear of the body causes the pressure drag. As the cross-sectional area of the body increases, the pressure drag also increases. The friction drag is also present in bluff bodies, but it is relatively small compared to the pressure drag.

Bluff bodies have a higher pressure drag coefficient than streamlined bodies, which have a low drag coefficient due to their streamlined shape, and the fluid can flow smoothly over them without any separation. In other words, the pressure drag of a bluff body is more than the friction drag.

Conclusion

In conclusion, the correct answer to the question is option B) more. Bluff bodies have a high drag coefficient due to their shape, resulting in a larger wake behind them, creating a low-pressure region. As a result, the pressure drag is higher than the friction drag.

The correct answer is option 'B': Viscosity of gas increases with an increase in temperature.

Viscosity is the measure of a fluid's resistance to flow. It is a property that determines the internal frictional resistance of a gas to flow when subjected to shear stress. The viscosity of a gas is influenced by various factors, including temperature and pressure.

Effect of Temperature on Viscosity:
When the temperature of a gas increases, the viscosity also increases. This is because as the temperature rises, the kinetic energy of the gas molecules also increases. The increased kinetic energy causes the gas molecules to move faster and collide with each other more frequently and with greater force. These collisions result in increased intermolecular interactions and stronger bonds between the gas molecules, leading to an increase in viscosity.

Explanation:
1. Gas Molecules and Kinetic Energy:
- Gas molecules are in constant random motion due to their kinetic energy.
- The kinetic energy of gas molecules is directly related to temperature. As temperature increases, the kinetic energy of the gas molecules also increases.
- This increased kinetic energy causes the gas molecules to move faster and collide more frequently.

2. Collisions and Intermolecular Interactions:
- When gas molecules collide, they exert forces on each other.
- These collision forces are responsible for the internal frictional resistance within the gas, which determines its viscosity.
- At higher temperatures, the increased kinetic energy of the gas molecules leads to more frequent and stronger collisions.
- These collisions result in increased intermolecular interactions and stronger bonds between the gas molecules.

3. Increased Viscosity:
- The increased intermolecular interactions and stronger bonds between gas molecules at higher temperatures result in an increase in viscosity.
- The gas molecules experience greater resistance to flow due to the increased intermolecular forces.
- This increased resistance leads to a higher viscosity of the gas.

Conclusion:
In summary, the correct option is 'B': Viscosity of gas increases with an increase in temperature. This is because the increased kinetic energy of gas molecules at higher temperatures leads to more frequent and stronger collisions, resulting in increased intermolecular interactions and higher viscosity.

The runaway speed of a hydraulic turbine refers to the speed at which the turbine runner is allowed to revolve freely without any load and with the wicket gates wide open. This speed is typically higher than the full load speed of the turbine and is an important parameter to consider in the design and operation of hydraulic turbines.

Explanation:
1. Full Load Speed:
- The full load speed of a hydraulic turbine refers to the speed at which the turbine operates when it is under full load conditions.
- It is the speed at which the turbine produces its rated power output.
- The full load speed is determined by the design and operating conditions of the turbine.

2. Speed at which Turbine Runner will be Damaged:
- This refers to the speed at which the turbine runner, which is the rotating component of the turbine, will be damaged or fail.
- If the turbine operates at a speed higher than its design limits, the runner can experience excessive centrifugal forces, which can lead to failure or damage.
- It is important to operate the turbine within its safe speed limits to avoid any potential damage to the runner.

3. Runaway Speed with Wicket Gates Wide Open:
- The runaway speed of a hydraulic turbine is the speed at which the turbine runner is allowed to revolve freely without any load and with the wicket gates wide open.
- With the wicket gates fully open, the water flow into the turbine is unrestricted, and the turbine can rotate at its maximum speed.
- The runaway speed is typically higher than the full load speed, as it represents the maximum speed that the turbine can attain under no load conditions.

4. Speed Corresponding to Maximum Overload Permissible:
- The speed corresponding to the maximum overload permissible refers to the maximum speed at which the turbine can operate under overload conditions.
- This speed is determined by the mechanical strength and design limits of the turbine components.
- Operating the turbine at speeds higher than the maximum overload permissible can lead to excessive stresses and potential failure of the turbine.

Conclusion:
The correct answer is option 'C', which states that the runaway speed of a hydraulic turbine is the speed at which the turbine runner is allowed to revolve freely without any load and with the wicket gates wide open. It is important to operate the turbine within its safe speed limits to avoid any potential damage or failure.

Introduction to Mercury in Barometers
Mercury has been traditionally used in barometers due to its unique physical properties. Understanding why mercury is preferred can be broken down into several key points.
Density and Height of the Column
- High Density: Mercury is a very dense liquid (approximately 13.6 times denser than water). This high density allows for a shorter column of mercury to measure atmospheric pressure effectively.
- Reduced Height for High Pressure: Because of its density, a barometer using mercury can measure high atmospheric pressures with a relatively small height of the liquid column, typically around 760 mm at sea level. This is advantageous in terms of space and practicality.
Liquid Metal Properties
- Non-Volatile and Stable: As a liquid metal, mercury does not evaporate easily, ensuring that the measurements remain stable over time without significant changes due to evaporation.
- Low Temperature Variation: Mercury's volume changes very little with temperature compared to other liquids, which ensures that temperature variations do not significantly affect the pressure readings.
Practical Considerations
- Visibility: The shiny surface of mercury makes it easy to read the height of the liquid column.
- Inertness: Mercury is chemically inert with most substances, reducing the risk of contamination or reactions that could affect measurements.
Conclusion
In summary, the primary reason mercury is used in barometers is option D, as its high density allows for a smaller column height to effectively measure high atmospheric pressure. Its unique properties make it an ideal choice for accurate and reliable measurements in meteorology.

Compressibility

Compressibility refers to the ability of a fluid to change its volume in response to a pressure change. When a fluid flows through a resistance, such as a pipe or a valve, it experiences a change in pressure which can result in a volumetric change of the fluid.

Volumetric Change

The volumetric change of the fluid is directly related to its compressibility. A fluid with high compressibility will undergo a significant change in volume when subjected to a pressure change, while a fluid with low compressibility will experience minimal volumetric change.

Resistance

The resistance encountered by the fluid can be due to various factors such as friction, obstructions, or changes in flow direction. This resistance causes a pressure drop in the fluid, which in turn leads to a change in volume.

Effect on the System

The volumetric change of the fluid caused by resistance can have implications for the overall system performance. It can affect the flow rate, efficiency, and pressure distribution within the system. Understanding the compressibility of the fluid is important for accurately predicting and analyzing the behavior of the system.

In conclusion, the volumetric change of the fluid caused by a resistance is closely tied to its compressibility. By considering the compressibility of the fluid, engineers can better design and optimize systems to account for changes in volume resulting from resistance.

Introduction:
Kinematic viscosity is a measure of a fluid's resistance to flow under the influence of gravity. It is defined as the ratio of dynamic viscosity to density. In simpler terms, it indicates how easily a fluid flows. The kinematic viscosity of a fluid depends on its molecular structure and temperature.

Kinematic viscosity of water:
Water is a common fluid with a relatively low kinematic viscosity. At 20°C, the kinematic viscosity of water is about 1.003 × 10^-6 m^2/s. This means that water flows easily compared to other fluids with higher kinematic viscosities.

Kinematic viscosity of mercury:
Mercury, on the other hand, has a much higher kinematic viscosity compared to water. At 20°C, the kinematic viscosity of mercury is about 1.53 × 10^-7 m^2/s. This makes mercury less flowable compared to water. Due to its higher kinematic viscosity, mercury tends to flow more slowly and is more resistant to flow.

Comparison between water and mercury:
When comparing water to mercury, it is evident that water has a higher kinematic viscosity than mercury. This means that water flows more easily compared to mercury. The lower kinematic viscosity of water is due to its molecular structure, which allows for freer movement of water molecules compared to the larger and heavier mercury molecules.

Temperature effect:
It is important to note that the kinematic viscosity of both water and mercury is temperature-dependent. As temperature increases, the kinematic viscosity of both fluids decreases. This is because the increase in temperature causes the fluid molecules to move more rapidly, reducing their internal friction and hence decreasing their resistance to flow.

Conclusion:
In conclusion, the kinematic viscosity of water is higher than that of mercury. Water flows more easily due to its lower kinematic viscosity. However, it is important to consider that the kinematic viscosity of both fluids is temperature-dependent, and as temperature increases, their kinematic viscosity decreases.

Flow past an airfoil
Friction drag is generally larger than pressure drag in flow past an airfoil due to the complex flow patterns and separation that occur around the airfoil shape. When air flows over an airfoil, the boundary layer near the surface of the airfoil experiences shear stress, resulting in friction drag. This friction drag is caused by the viscosity of the air and the resistance it exerts on the surface of the airfoil.

Pressure drag
On the other hand, pressure drag is related to the pressure difference between the front and rear of the airfoil. This pressure difference creates resistance to the flow of air and contributes to the overall drag force experienced by the airfoil. In flow past an airfoil, the pressure drag is generally less significant compared to the friction drag.

Effect of shape
The shape of an airfoil, with its curved surfaces and varying thickness, contributes to the development of turbulent boundary layers and separation points, which in turn increase the friction drag. The pressure distribution around an airfoil also plays a role in determining the overall drag characteristics.

Conclusion
Overall, in flow past an airfoil, the friction drag is typically larger than the pressure drag due to the complex flow phenomena and boundary layer effects associated with the airfoil shape. Understanding these drag components is essential for optimizing the design and performance of airfoil shapes in various engineering applications.

Introduction:
In a pipeline system, vaporization can occur due to the pressure drop along the pipeline. This vaporization can lead to problems such as cavitation, which can cause damage to the pipeline and reduce its efficiency. To avoid vaporization, the pipeline is laid at a certain height above the hydraulic gradient.

Explanation:
The hydraulic gradient is the slope of the hydraulic grade line, which represents the energy or pressure in the pipeline system. To avoid vaporization in the pipeline, it is important to ensure that the pressure in the pipeline does not drop below the vapor pressure of the fluid being transported.

Importance of pipeline height:
The height at which the pipeline is laid above the hydraulic gradient determines the pressure difference between the fluid in the pipeline and the surrounding atmosphere. This pressure difference affects the vaporization potential in the pipeline.

Maximum height to avoid vaporization:
Option B states that the pipeline should not be laid more than 6.4 m above the hydraulic gradient to avoid vaporization. This means that the pressure in the pipeline should not drop more than the equivalent pressure of a 6.4 m column of fluid.

Reason behind the maximum height limit:
If the pipeline is laid too high above the hydraulic gradient, the pressure drop along the pipeline will be significant. This pressure drop can cause the pressure in the pipeline to drop below the vapor pressure of the fluid. When this happens, the fluid will start to vaporize, leading to cavitation and other related issues.

Other options:
Option A states that the maximum height should be 2.4 m above the hydraulic gradient. This limit may not be sufficient to prevent vaporization in all cases, especially if the pressure drop along the pipeline is significant.

Option C states that the maximum height should be 10.0 m above the hydraulic gradient. This limit may be unnecessarily conservative and may result in higher construction costs for the pipeline.

Option D states that the maximum height should be 5.0 m above the hydraulic gradient. This limit is lower than option B and may not provide sufficient safety margin to prevent vaporization.

Conclusion:
To avoid vaporization in the pipeline, it is recommended to lay the pipeline at a height not more than 6.4 m above the hydraulic gradient. This limit ensures that the pressure in the pipeline does not drop below the vapor pressure of the fluid, preventing vaporization and related issues.

Shear Stress and Deformation in a Fluid

The given question asks when a fluid will deform under the action of a shear stress. Let's examine the options and explain why option 'B' is the correct answer.

Option A: When the applied shear stress is greater than the weight of the fluid
This option is not correct because the weight of the fluid is not directly related to its deformation under shear stress. The weight of the fluid only affects its behavior under gravity, not under shear stress.

Option B: When the applied shear stress is greater than the viscous strength of the fluid
This option is correct. When a fluid is subjected to shear stress, its response depends on its viscous strength. Viscosity is a measure of a fluid's resistance to flow. When the applied shear stress exceeds the viscous strength of the fluid, it will deform and flow.

Option C: When the applied shear stress is greater than the yield strength of the fluid
This option is not applicable to fluids. Yield strength is a property of solid materials and refers to the stress at which plastic deformation begins. Fluids, on the other hand, do not exhibit yield strength as they can continuously deform under shear stress without undergoing plastic deformation.

Option D: Independent of the rate of shear strain
This option is not correct. The rate of shear strain refers to the speed at which the fluid is being deformed. The deformation response of a fluid under shear stress is highly dependent on the rate of shear strain. Different fluids may exhibit different behaviors at different shear strain rates.

Conclusion:
When a fluid is acted upon by a shear stress, it will deform and flow when the applied shear stress is greater than the viscous strength of the fluid. This behavior is due to the fluid's resistance to flow, known as its viscosity. The weight of the fluid and the yield strength of the fluid are not directly related to its deformation under shear stress. Additionally, the rate of shear strain has a significant impact on the fluid's deformation response.

Explanation:

An accumulator is a device used in hydraulic systems to store and release energy. It acts as a supplementary energy source in case of machines that work intermittently or require additional energy to supplement the discharge from the normal source.

1. Purpose of an Accumulator:
- The main purpose of an accumulator is to store energy in the form of pressurized fluid (usually hydraulic fluid) and release it when needed.
- It helps in maintaining a steady and constant fluid pressure in the hydraulic system, compensating for any fluctuations in demand or supply.

2. Working Principle:
- The accumulator consists of a cylindrical chamber divided into two sections by a movable piston or bladder.
- One section is filled with hydraulic fluid, while the other section is filled with an inert gas (usually nitrogen) under pressure.
- When the hydraulic system is operating, the hydraulic fluid enters the accumulator, compressing the gas and storing energy.
- When the system requires additional energy, the compressed gas expands, forcing the stored hydraulic fluid back into the system.

3. Types of Accumulators:
There are different types of accumulators, including:
- Piston Accumulator: It uses a piston to separate the gas and fluid chambers.
- Bladder Accumulator: It uses a flexible bladder to separate the gas and fluid chambers.
- Diaphragm Accumulator: It uses a diaphragm to separate the gas and fluid chambers.

4. Use in Intermittent Machines:
- Intermittent machines, such as presses, require a high amount of energy during specific operations but operate intermittently.
- The accumulator helps supply the required energy during peak demand periods when the normal energy source may not be sufficient.
- It ensures that the machine operates smoothly and efficiently without overloading the primary power source.

5. Supplementing Discharge:
- In some machines, the discharge from the normal energy source may not be sufficient to meet the desired output or performance.
- The accumulator acts as a supplement by providing additional energy to meet the high-demand periods.
- It helps in improving the overall performance and efficiency of the machine.

In conclusion, an accumulator is a device that stores energy in hydraulic systems and releases it when needed. It is used in machines that work intermittently or require additional energy to supplement the discharge from the normal energy source. By providing supplementary energy, the accumulator ensures smooth operation and improved performance of the machines.