Reynolds number and its significance MCQs With Answer

Reynolds number and its significance MCQs With Answer

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Reynolds number and its significance MCQs With Answer

Reynolds number (Re) is a fundamental dimensionless parameter in fluid mechanics that quantifies the ratio of inertial to viscous forces in a flow. For B. Pharm students, understanding Re is crucial for pharmaceutical unit operations such as mixing, spray drying, tablet coating, aerosol generation, and scale-up of processes. Reynolds influences flow regimes (laminar, transitional, turbulent), mass and heat transfer rates, particle behavior, and equipment design. Mastery of Re, its calculation using density, velocity, characteristic length and viscosity, and its practical implications helps optimize formulation processing, predict scale-up behavior, and ensure reproducible drug product quality. Now let’s test your knowledge with 50 MCQs on this topic.

Q1. What is the standard definition of Reynolds number (Re)?

  • The ratio of inertial forces to gravitational forces
  • The ratio of viscous forces to inertial forces
  • The ratio of inertial forces to viscous forces
  • The product of velocity and viscosity

Correct Answer: The ratio of inertial forces to viscous forces

Q2. Which formula correctly represents Reynolds number for flow of a Newtonian fluid in a pipe?

  • Re = (rho × V × L) / mu
  • Re = mu / (rho × V × L)
  • Re = (rho × mu) / (V × L)
  • Re = (V × L) / (rho × mu)

Correct Answer: Re = (rho × V × L) / mu

Q3. Which alternative form of Reynolds number uses kinematic viscosity (ν)?

  • Re = V × L × ν
  • Re = V × L / ν
  • Re = ν / (V × L)
  • Re = V / (L × ν)

Correct Answer: Re = V × L / ν

Q4. For internal flow in a circular pipe, approximately which Re value indicates laminar flow?

  • Re < 2000
  • Re > 4000
  • Re between 4000 and 10000
  • Re ≈ 100000

Correct Answer: Re < 2000

Q5. For internal flow in a circular pipe, which Re range typically indicates fully turbulent flow?

  • Re < 200
  • 2000 < Re < 4000
  • Re > 4000
  • Re between 100 and 500

Correct Answer: Re > 4000

Q6. What characteristic length should you choose when calculating Re for flow around a spherical particle?

  • Particle radius
  • Particle diameter
  • Pipe diameter
  • Viscosity

Correct Answer: Particle diameter

Q7. Which statement best explains the physical meaning of a very low Reynolds number (Re ≪ 1)?

  • Inertial forces dominate and flow is highly turbulent
  • Viscous forces dominate and flow is in the Stokes (creeping) regime
  • Flow is dominated by gravitational effects
  • Flow will always separate from the surface

Correct Answer: Viscous forces dominate and flow is in the Stokes (creeping) regime

Q8. How is Reynolds number useful in pharmaceutical scale-up of mixing processes?

  • It ensures identical dimensions of equipment only
  • It helps maintain dynamic similarity of flow regimes and mixing characteristics
  • It replaces the need to measure viscosity
  • It determines chemical stability of APIs

Correct Answer: It helps maintain dynamic similarity of flow regimes and mixing characteristics

Q9. Which of the following is TRUE about the units of Reynolds number?

  • It has units of kg·m−1·s−1
  • It is dimensionless
  • It has units of m/s
  • It has units of Pascal

Correct Answer: It is dimensionless

Q10. For flow over a flat plate, the approximate Reynolds number at which transition to turbulence typically occurs (based on plate length) is:

  • ReL ≈ 5 × 10^2
  • ReL ≈ 5 × 10^3
  • ReL ≈ 5 × 10^5
  • ReL ≈ 5 × 10^7

Correct Answer: ReL ≈ 5 × 10^5

Q11. Which dimensionless number relates Reynolds number and mass transfer through the relation Pe = Re × Sc?

  • Peclet number (Pe)
  • Prandtl number (Pr)
  • Biot number (Bi)
  • Damköhler number (Da)

Correct Answer: Peclet number (Pe)

Q12. In stirred tanks, which characteristic length is commonly used to compute Re?

  • Tank height
  • Impeller diameter
  • Nozzle length
  • Viscosity

Correct Answer: Impeller diameter

Q13. If density increases while velocity, length and viscosity remain constant, Reynolds number will:

  • Decrease
  • Remain constant
  • Increase
  • Become dimensionful

Correct Answer: Increase

Q14. Which factor does NOT directly influence Reynolds number?

  • Characteristic length
  • Fluid density
  • Fluid color
  • Fluid viscosity

Correct Answer: Fluid color

Q15. In flow through porous media or packed beds, which modified Reynolds number or correlation often appears?

  • Grashof number
  • Ergun/packed-bed Reynolds number
  • Biot-Reynolds correlation
  • Weber number

Correct Answer: Ergun/packed-bed Reynolds number

Q16. For a sphere at very low Reynolds numbers, the drag coefficient (Cd) approximately follows which relation?

  • Cd ≈ 24 / Re
  • Cd ≈ Re / 24
  • Cd ≈ constant ≈ 1.0
  • Cd ∝ Re^2

Correct Answer: Cd ≈ 24 / Re

Q17. Which practical pharmaceutical process is most sensitive to changes in Reynolds number?

  • Tablet printing color selection
  • Mixing and homogeneity in liquid formulations
  • API molecular weight determination
  • Packaging label design

Correct Answer: Mixing and homogeneity in liquid formulations

Q18. In aerosol and inhaler design, why is Reynolds number important?

  • It directly gives drug potency
  • It influences droplet breakup, aerosolization and dispersion patterns
  • It measures dissolution rate in stomach
  • It determines taste masking effectiveness

Correct Answer: It influences droplet breakup, aerosolization and dispersion patterns

Q19. Which change will decrease Reynolds number for a given flow?

  • Increase fluid velocity
  • Decrease characteristic length
  • Decrease fluid viscosity
  • Increase fluid density

Correct Answer: Decrease characteristic length

Q20. For non-Newtonian fluids, computing Reynolds number requires:

  • Use of constant dynamic viscosity only
  • An apparent or effective viscosity definition appropriate to the shear rate
  • Ignoring viscosity altogether
  • Doubling the Newtonian Re always

Correct Answer: An apparent or effective viscosity definition appropriate to the shear rate

Q21. Which Reynolds number value is associated with the “creeping flow” regime relevant to microfluidics?

  • Re ≈ 10^6
  • Re ≈ 10^3
  • Re ≪ 1
  • Re ≈ 5000

Correct Answer: Re ≪ 1

Q22. Which characteristic velocity should be used when calculating Re for flow through a pipe?

  • Maximum local velocity at the wall
  • Mean (average) velocity in the pipe
  • Speed of sound
  • Surface tension divided by density

Correct Answer: Mean (average) velocity in the pipe

Q23. Reynolds number plays a direct role in which of the following heat/mass transfer correlations?

  • Nernst equation
  • Nusselt/Reynolds/Prandtl type correlations
  • Henderson-Hasselbalch equation
  • Michaelis-Menten kinetics

Correct Answer: Nusselt/Reynolds/Prandtl type correlations

Q24. Typical Reynolds number range for blood flow in large arteries is approximately:

  • Re > 10000
  • Re ≈ 1000
  • Re ≪ 1
  • Re = 0

Correct Answer: Re ≈ 1000

Q25. Which dimensionless number is most relevant when combining Reynolds and viscous diffusion time scales for mass transfer?

  • Schmidt number (Sc)
  • Refractive index
  • Henry’s constant
  • pKa

Correct Answer: Schmidt number (Sc)

Q26. In spray drying and atomization, increasing Reynolds number typically leads to:

  • More stable, larger droplets only
  • Enhanced atomization and finer droplets under same conditions
  • No effect on droplet size
  • Complete suppression of evaporation

Correct Answer: Enhanced atomization and finer droplets under same conditions

Q27. Which of the following correctly expresses Reynolds number units (if any)?

  • m2/s
  • kg·m−3
  • No units (dimensionless)
  • Pa·s

Correct Answer: No units (dimensionless)

Q28. When scaling up a reactor while keeping Reynolds number constant, which condition is implied?

  • Geometric similarity and dynamic similarity of flow
  • Chemical reaction rates will always increase
  • Temperature is irrelevant
  • Viscosity must be zero

Correct Answer: Geometric similarity and dynamic similarity of flow

Q29. Which Reynolds number definition is most appropriate for flow in a non-circular duct?

  • Use hydraulic diameter as the characteristic length
  • Always use duct width regardless of shape
  • Use fluid color as length scale
  • Re is not defined for non-circular ducts

Correct Answer: Use hydraulic diameter as the characteristic length

Q30. Which of the following best describes the transitional Reynolds number range in a circular pipe?

  • Re between 0 and 1
  • Re between 2000 and 4000
  • Re between 10000 and 20000
  • Re above 1 million

Correct Answer: Re between 2000 and 4000

Q31. For a given pipe flow, doubling the fluid velocity will change Reynolds number by what factor?

  • It will halve Re
  • It will double Re
  • It will quadruple Re
  • No change in Re

Correct Answer: It will double Re

Q32. Which pharmaceutical application often operates under laminar flow conditions due to small length scales?

  • Bulk powder blending in large bins
  • Microfluidic drug formulation and lab-on-a-chip devices
  • Large-scale stirred tank mixing of high velocity streams
  • Spray coating in industrial dryers

Correct Answer: Microfluidic drug formulation and lab-on-a-chip devices

Q33. In Ergun equation for packed beds, the Reynolds number used is based on:

  • Superficial velocity and particle diameter
  • Sound speed and bed height
  • Impeller diameter
  • Concentration of API

Correct Answer: Superficial velocity and particle diameter

Q34. Which experimental parameter would you adjust to increase Re during a dissolution test?

  • Decrease paddle rotation speed
  • Increase paddle rotation speed
  • Decrease medium density only
  • Increase tablet hardness without changing flow

Correct Answer: Increase paddle rotation speed

Q35. Which statement about Reynolds number in oscillatory or pulsatile flows (e.g., blood) is correct?

  • Re is irrelevant for oscillatory flows
  • Pulsatility introduces additional dimensionless groups but Re still characterizes inertial/viscous balance
  • Re always becomes zero in pulsatile flows
  • Only Grashof number matters

Correct Answer: Pulsatility introduces additional dimensionless groups but Re still characterizes inertial/viscous balance

Q36. If dynamic viscosity (mu) increases while other parameters remain constant, Reynolds number will:

  • Increase proportionally
  • Decrease
  • Remain unchanged
  • Become negative

Correct Answer: Decrease

Q37. Which relation links drag coefficient for a sphere and Reynolds number in the Stokes regime?

  • Cd ≈ 24 / Re
  • Cd ≈ Re / 24
  • Cd ≈ constant 0.5
  • Cd ∝ Re^3

Correct Answer: Cd ≈ 24 / Re

Q38. Calculate Re for water (rho = 1000 kg/m3, mu = 0.001 Pa·s) in a pipe with mean velocity 0.2 m/s and diameter 0.01 m.

  • Re = 20
  • Re = 200
  • Re = 2000
  • Re = 20000

Correct Answer: Re = 2000

Q39. Using kinematic viscosity ν = 1×10−6 m2/s, calculate Re for V = 0.5 m/s and L = 0.02 m.

  • Re = 10
  • Re = 100
  • Re = 10,000
  • Re = 1,000,000

Correct Answer: Re = 10,000

Q40. In the design of inhalers, a higher Reynolds number inside the device typically indicates:

  • Less particle or droplet breakup and coarser aerosol
  • Greater inertial impaction and potential deposition in mouth-throat
  • No change in deposition patterns
  • Lower chances of delivery to lungs

Correct Answer: Greater inertial impaction and potential deposition in mouth-throat

Q41. Which dimensionless number should be considered alongside Reynolds when surface tension effects are important in droplet formation?

  • Weber number
  • Biot number
  • Péclet number
  • Schmidt number

Correct Answer: Weber number

Q42. For flow through a very narrow capillary used in HPLC, typical Reynolds numbers are:

  • Very high (≫10^5)
  • Moderate (≈10^3–10^4)
  • Very low (≪1) — laminar
  • Undefined

Correct Answer: Very low (≪1) — laminar

Q43. Which phenomenon is more likely to occur as Reynolds number increases around a bluff body like a cylinder?

  • Flow becomes more steady and attached
  • Onset of vortex shedding and wake instabilities
  • Viscous damping eliminates wakes
  • Surface tension dominates flow

Correct Answer: Onset of vortex shedding and wake instabilities

Q44. In the context of drug formulation, why might non-Newtonian rheology change effective Reynolds number?

  • Because non-Newtonian fluids are always Newtonian at high shear
  • Because the apparent viscosity depends on shear rate, altering Re calculation
  • Non-Newtonian behavior does not affect Re
  • Because density becomes zero

Correct Answer: Because the apparent viscosity depends on shear rate, altering Re calculation

Q45. Which of these is a correct strategy to achieve similar heat transfer performance between model and prototype systems?

  • Match Reynolds and Prandtl numbers between model and prototype
  • Match only the geometric size
  • Match only temperature
  • Ignore Re and use visual similarity only

Correct Answer: Match Reynolds and Prandtl numbers between model and prototype

Q46. Which Reynolds-based correlation is commonly used to estimate pressure drop in laminar flow through a circular pipe?

  • Hagen–Poiseuille equation (linked to low Re laminar)
  • Bernoulli’s equation for turbulent flow
  • Ergun equation only for dilute gas
  • Navier-Stokes cannot be simplified

Correct Answer: Hagen–Poiseuille equation (linked to low Re laminar)

Q47. The Reynolds number for flow around a droplet will influence which of the following during spray drying?

  • Droplet heating rate only
  • Atomization regime, breakup mechanism and subsequent drying
  • Only solubility of API
  • Viscosity of the solid product

Correct Answer: Atomization regime, breakup mechanism and subsequent drying

Q48. For flow past a flat plate, the local Reynolds number is based on:

  • Plate thickness
  • Distance from the leading edge
  • Plate color
  • Fluid surface tension

Correct Answer: Distance from the leading edge

Q49. Which of the following gives a correct interpretation when Re = 0 for an idealized case?

  • Flow is dominated entirely by inertial forces
  • There is no inertia; purely viscous, quasi-static conditions (theoretical limit)
  • Flow is extremely turbulent
  • Re = 0 is physically impossible in all cases

Correct Answer: There is no inertia; purely viscous, quasi-static conditions (theoretical limit)

Q50. Which combination of modifications would increase Reynolds number in an industrial coating line?

  • Reduce line speed and increase fluid viscosity
  • Increase line speed and reduce fluid viscosity
  • Reduce nozzle diameter and increase viscosity
  • Decrease temperature to raise viscosity and decrease speed

Correct Answer: Increase line speed and reduce fluid viscosity

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