Similitude in Fluid Mechanics: Master the Art of Scaling Fluid Flow Systems

Question 1

When comparing geometrically similar fluid flow systems, the ratio of their linear dimensions is referred to as:

Accepted Answer

Scale factor

Answer

Similarity ratio

Answer

Dimensionless number

Answer

Reynolds number

Question 2

The Reynolds number is a dimensionless number that represents the:

Accepted Answer

Ratio of inertial to viscous forces

Answer

Ratio of gravitational to viscous forces

Answer

Ratio of pressure to viscous forces

Answer

Ratio of surface tension to viscous forces

Question 3

The practice of comparing fluid flow systems using dimensionless numbers is known as:

Accepted Answer

Similitude analysis

Answer

Dimensional analysis

Answer

Buckingham Pi analysis

Answer

Reynolds number analysis

Question 4

Which of the following is not considered a type of similitude used in fluid mechanics?

Accepted Answer

Chemical similitude

Answer

Dynamic similitude

Answer

Kinematic similitude

Answer

Geometric similitude

Question 5

According to the Buckingham Pi Theorem, the number of dimensionless groups formed from a set of variables is equal to:

Accepted Answer

The difference between the number of variables and fundamental dimensions

Answer

The sum of the number of variables and fundamental dimensions

Answer

The number of variables

Answer

The number of fundamental dimensions

Question 6

A model of a submarine is tested in a towing tank at a scale of 1:25. If the submarine has a length of 120 m and a speed of 30 knots in the prototype, what is the corresponding speed in the model?

Accepted Answer

6 knots

Answer

12 knots

Answer

18 knots

Answer

24 knots

Question 7

The dimensionless number characterizing the ratio of inertial forces to gravitational forces in a fluid flow system is:

Accepted Answer

Froude number

Answer

Reynolds number

Answer

Weber number

Answer

Strouhal number

Question 8

In similitude, the geometric similarity ratio ensures:

Accepted Answer

Proportional shapes and dimensions between the physical model and prototype

Answer

Matching flow velocities and pressure gradients between the model and prototype

Answer

Equal Reynolds numbers between the model and prototype

Answer

Identical fluid properties between the model and prototype

Question 9

The key distinction between physical modeling and mathematical modeling in similitude is that:

Accepted Answer

Physical modeling involves constructing a scaled model, while mathematical modeling involves developing mathematical representations

Answer

Physical modeling is more accurate than mathematical modeling

Answer

Mathematical modeling is more versatile than physical modeling

Answer

Physical modeling is limited to steady-state conditions, while mathematical modeling can handle both steady-state and unsteady-state conditions

Question 10

Identify the quantity that is NOT considered dimensionless:

Accepted Answer

Velocity

Answer

Reynolds number

Answer

Froude number

Question 11

According to the Buckingham Pi theorem, the number of dimensionless groups necessary to represent a physical phenomenon is equal to:

Accepted Answer

Number of variables minus the number of fundamental dimensions

Answer

Number of variables plus the number of fundamental dimensions

Answer

Number of variables divided by the number of fundamental dimensions

Question 12

What is the primary purpose of using scale models in similitude?

Accepted Answer

Predicting the behavior of a larger-scale system by studying a smaller-scale model

Answer

Designing a system that is identical in size to the prototype

Answer

Verifying the results of computational fluid dynamics simulations

Question 13

What is the significance of scale factors in similitude?

Accepted Answer

Ensuring that dimensionless groups are identical for the model and prototype systems

Answer

Enlarging the model system relative to the prototype

Answer

Reducing the size of the model system relative to the prototype

Question 14

Identify a limitation of similitude modeling:

Accepted Answer

Inability to account for all physical effects

Answer

Guaranteed accuracy

Answer

High computational cost

Answer

Simplicity in application

Question 15

What is the physical interpretation of the Reynolds number?

Accepted Answer

Ratio of inertial forces to viscous forces in a fluid flow

Answer

Ratio of pressure forces to viscous forces in a fluid flow

Question 16

What is the physical interpretation of the Froude number?

Accepted Answer

Ratio of inertial forces to gravitational forces in a fluid flow

Answer

Ratio of pressure forces to gravitational forces in a fluid flow

Question 17

What is the physical interpretation of the Mach number?

Accepted Answer

Ratio of inertial forces to compressibility forces in a fluid flow

Answer

Ratio of pressure forces to compressibility forces in a fluid flow

Question 18

According to the Buckingham Pi theorem, the number of dimensionless groups in a fluid flow system is equal to:

Accepted Answer

The number of variables minus the number of fundamental dimensions

Answer

The number of variables plus the number of fundamental dimensions

Question 19

In a model fluid flow system, the scale ratio for velocity is:

Accepted Answer

Square root of the scale ratio for length

Answer

Scale ratio for length

Answer

Inverse of the scale ratio for length

Answer

Cube root of the scale ratio for length

Question 20

Which of the following is a limitation of similitude?

Accepted Answer

Cannot account for differences in fluid properties between the model and prototype

Answer

Always provides accurate predictions

Answer

Can be applied to any fluid flow system

Question 21

The Reynolds number represents the ratio of:

Accepted Answer

Inertial forces to viscous forces

Answer

Gravitational forces to viscous forces

Answer

Pressure forces to viscous forces

Answer

Surface tension forces to viscous forces

Question 22

For similitude to be valid, which conditions must be satisfied?

Accepted Answer

Geometric similarity, kinematic similarity, and dynamic similarity

Answer

Kinematic similarity and dynamic similarity

Answer

Geometric similarity and kinematic similarity

Question 23

Similitude is a valuable tool in fluid mechanics because it allows us to:

Accepted Answer

Predict the behavior of complex fluid flow systems based on simpler models

Answer

Design fluid flow systems without any experimental testing

Answer

Eliminate the need for computational fluid dynamics