Match the following and select the correct answer from the codes given below the lists List I List II A. Steam Nozzle 1. Mach number B. Compressible flow 2. Reaction turbine C. Surface Tension 3. Biot number D. Heat conduction 4. Nusselt number 5. Supersaturation 6. Weber number
Understanding Fluid Mechanics and Heat Transfer Concepts
This question asks us to match concepts from List I related to fluid mechanics and heat transfer phenomena with relevant terms or dimensionless numbers from List II. Let's analyze each item in List I and find its corresponding match in List II based on fundamental principles.
Matching List I to List II
Let's go through each item in List I and find the best fit from List II:
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A. Steam Nozzle:
Steam nozzles are devices used to expand steam and accelerate it to high velocities. During rapid expansion, the steam's pressure and temperature drop. If the process is fast enough, the steam may cool below its saturation temperature corresponding to the local pressure without condensing immediately. This metastable state is known as Supersaturation. Therefore, Steam Nozzle is closely associated with Supersaturation.
Match: A - 5
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B. Compressible flow:
Compressible flow is the flow of fluids (typically gases) where changes in density are significant. This usually occurs at high speeds. The Mach number is a crucial dimensionless quantity in compressible flow, defined as the ratio of the speed of the flow (\(V\)) to the speed of sound (\(a\)) in the medium: \( M = \frac{V}{a} \). It indicates whether the flow is subsonic (\(M < 1\)), sonic (\(M = 1\)), or supersonic (\(M > 1\)).
Match: B - 1
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C. Surface Tension:
Surface tension is a property of liquids that causes the surface to behave like a stretched elastic membrane. It results from the cohesive forces between liquid molecules. The Weber number is a dimensionless quantity used in fluid mechanics to characterize the relative importance of inertial forces compared to surface tension forces at an interface between two fluids. It is defined as \( We = \frac{\rho V^2 L}{\sigma} \), where \(\rho\) is density, \(V\) is velocity, \(L\) is characteristic length, and \(\sigma\) is surface tension.
Match: C - 6
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D. Heat conduction:
Heat conduction is the transfer of thermal energy through a substance due to a temperature difference, without bulk movement of the material. In heat transfer analysis, dimensionless numbers help characterize different heat transfer modes. The Biot number is a dimensionless quantity used in transient heat conduction problems. It is defined as \( Bi = \frac{hL}{k} \), where \(h\) is the convective heat transfer coefficient at the surface, \(L\) is a characteristic length of the solid, and \(k\) is the thermal conductivity of the solid. The Biot number compares the internal thermal resistance of a solid body to the thermal resistance at its surface due to convection.
Match: D - 3
Summary Table
Based on the analysis, the correct matches are:
| List I | List II | Match |
|---|---|---|
| A. Steam Nozzle | 5. Supersaturation | A - 5 |
| B. Compressible flow | 1. Mach number | B - 1 |
| C. Surface Tension | 6. Weber number | C - 6 |
| D. Heat conduction | 3. Biot number | D - 3 |
This gives the combination A - 5, B - 1, C - 6, D - 3.
Important Questions from Dimensionless Number
The Reynold’s number, used for critical velocity for turbulent flow of fluids, is given by the relation
Reynolds number for non - circular cross-section is:
[V = mean velocity, ν = kinematic viscosity, P = ratio of cross-sectional area to the wetted perimeter]
A) \(V.\frac{{4P}}{v}\)
B) \(\frac{{V.P}}{v}\)
C) \(\frac{{V.2P}}{{4v}}\)
D) \(\frac{{V.P}}{{4v}}\)
When the Mach number is less than unity, the flow is
The only possible dimensionless group that combines velocity ‘V’, body size ‘L’, fluid density ‘ρ’ & surface tension ‘σ’
- Which of the following is not a non-dimensional parameter?
