# Dimensional and Model Analysis MCQs - Fluid Mechanics

Dimensional and Model Analysis MCQs - Fluid Mechanics: This section contains the multiple-choice questions and answers on the fluid mechanics chapter Dimensional and Model Analysis. practice these MCQs to learn and enhance the knowledge of Dimensional and Model Analysis.

## List of Fluid Mechanics - Dimensional and Model Analysis MCQs

1. What is the purpose of dimensional analysis in fluid mechanics?

1. To simplify complex fluid flow problems
2. To obtain a set of dimensionless groups
3. To determine the absolute values of physical quantities
4. To solve equations numerically

Answer: B) To obtain a set of dimensionless groups

Explanation:

Dimensional analysis helps in obtaining dimensionless groups that represent the behavior of physical systems independent of units.

2. What is the primary advantage of using dimensionless groups in fluid mechanics analysis?

1. They simplify complex equations
2. They help in numerical integration
3. They provide absolute values of physical quantities
4. They eliminate the need for units

Answer: A) They simplify complex equations

Explanation:

Dimensionless groups simplify complex equations and make them easier to work with.

3. In dimensional analysis, what is the term "dimensional homogeneity" referring to?

1. The consistency of units in an equation
2. The behavior of fluid at high temperatures
3. The conservation of mass in fluid flow
4. The similarity between model and prototype

Answer: A) The consistency of units in an equation

Explanation:

Dimensional homogeneity refers to the consistency of units in an equation.

4. What is a derived quantity in dimensional analysis?

1. A dimensionless quantity
2. A quantity that is derived from the fundamental dimensions using mathematical operations
3. A quantity that depends on the density of the fluid only
4. A physical quantity that cannot be expressed using fundamental dimensions

Answer: B) A quantity that is derived from the fundamental dimensions using mathematical operations

Explanation:

Derived quantities are formed from fundamental dimensions using mathematical operations, such as multiplication, division, or exponentiation.

5. Which of the following is a derived quantity related to fluid dynamics?

1. Pressure
2. Density
3. Velocity
4. Viscosity

Explanation:

Velocity is a derived quantity in fluid dynamics as it involves the combination of length and time dimensions.

6. What is the main difference between fundamental and derived dimensions?

1. Fundamental dimensions are related to fluid properties, while derived dimensions are related to flow behavior
2. Derived dimensions are used in dimensionless groups, while fundamental dimensions are not
3. Fundamental dimensions are always dimensionless, while derived dimensions have units
4. Fundamental dimensions can be expressed in terms of derived dimensions

Answer: A) Fundamental dimensions are related to fluid properties, while derived dimensions are related to flow behavior.

Explanation:

Fundamental dimensions are related to basic properties like mass, length, and time, while derived measurements are formed by combining these fundamental dimensions to represent flow behavior in fluid mechanics.

7. Why is dimensional homogeneity essential in fluid mechanics?

1. It simplifies equations and enhances their physical meaning
2. It allows for the comparison of fluids with different properties
3. It eliminates the need for using any units in equations
4. It ensures that all fluid mechanics problems have the same solution

Answer: A) It simplifies equations and enhances their physical meaning.

Explanation:

Dimensional homogeneity simplifies equations and ensures that the physical meaning of equations remains intact, regardless of the choice of units.

8. Which of the following equations is dimensionally homogeneous?

1. V = IR
2. E = mc^2
3. P = F/A
4. F = ma

Explanation:

The equation P = F/A is dimensionally homogeneous because the dimensions of pressure (force per unit area) are consistent.

9. What is the primary objective of Buckingham's π theorem in fluid mechanics?

1. To calculate the exact numerical values of physical quantities
2. To identify the significant parameters and create dimensionless groups
3. To compare experimental results to theoretical predictions
4. To establish the absolute units for fluid properties

Answer: B) To identify the significant parameters and create dimensionless groups.

Explanation:

Buckingham's π theorem is used to identify the significant parameters and create dimensionless groups that simplify fluid mechanics problems.

10. Which of the following statements about Buckingham's π theorem is true?

1. It is only applicable to problems with a single dimensionless group
2. It is used primarily for numerical analysis in fluid mechanics
3. It helps in establishing the units of physical quantities
4. It provides a systematic way to identify dimensionless groups in fluid mechanics problems

Answer: D) It provides a systematic way to identify dimensionless groups in fluid mechanics problems.

Explanation:

Buckingham's π theorem provides a systematic way to identify dimensionless groups in fluid mechanics problems, aiding in their simplification and analysis.

11. What is the primary purpose of model analysis in fluid mechanics?

1. To create miniature versions of fluid systems
2. To study fluid behavior on a smaller scale
3. To validate the results of dimensional analysis
4. To determine the absolute values of physical quantities

Answer: B) To study fluid behavior on a smaller scale

Explanation:

Model analysis in fluid mechanics involves studying fluid behavior on a smaller scale to gain insights into larger systems.

12. Which type of similitude involves the preservation of both ratios of forces and ratios of linear dimensions between a model and a prototype?

1. Kinematic similarity
2. Dynamic similarity
3. Geometric similarity
4. Kinetic similarity

Explanation:

Dynamic similarity involves the preservation of both ratios of forces (like Reynolds number) and ratios of linear dimensions between the model and prototype.

13. Geometric similarity primarily focuses on preserving which aspect between a model and a prototype?

1. Ratios of forces
2. Ratios of linear dimensions
3. Ratios of fluid properties
4. Ratios of time scales

Answer: B) Ratios of linear dimensions

Explanation:

Geometric similarity focuses on preserving ratios of linear dimensions between the model and prototype.

14. What does the Reynolds number (Re) indicate in fluid mechanics?

1. The ratio of inertial forces to viscous forces
2. The ratio of elastic forces to inertial forces
3. The ratio of pressure forces to inertial forces
4. The ratio of gravitational forces to inertial forces

Answer: A) The ratio of inertial forces to viscous forces

Explanation:

The Reynolds number (Re) indicates the ratio of inertial forces to viscous forces in fluid flow.

15. Which dimensionless group characterizes the ratio of pressure gradient to viscous forces in fluid flow?

1. Euler number (Eu)
2. Weber number (We)
3. Mach number (Ma)
4. Reynolds number (Re)

Explanation:

The Euler number (Eu) characterizes the ratio of pressure gradient to viscous forces in fluid flow.

16. What is the Weber number (We) used to describe?

1. The ratio of inertial forces to surface tension forces
2. The ratio of the speed of sound to fluid velocity
3. The ratio of convective heat transfer to conductive heat transfer
4. The ratio of elastic forces to inertial forces

Answer: A) The ratio of inertial forces to surface tension forces

Explanation:

The Weber number (We) is used to describe the ratio of inertial forces to surface tension forces in fluid flow.

17. What does the Mach number (Ma) represent?

1. The ratio of inertial forces to viscous forces
2. The ratio of gravitational forces to inertial forces
3. The ratio of the speed of sound to fluid velocity
4. The ratio of pressure forces to inertial forces

Answer: C) The ratio of the speed of sound to fluid velocity

Explanation:

The Mach number (Ma) represents the ratio of the speed of sound to fluid velocity and is used to characterize compressible flow.