Master Dimensional Analysis in Fluid Mechanics: Enhance Problem-Solving Skills

Question 1

The relationship between the Reynolds number and the flow regime is that:

Accepted Answer

Laminar flow occurs at low Reynolds numbers, while turbulent flow occurs at high Reynolds numbers.

Answer

Turbulent flow occurs at low Reynolds numbers, while laminar flow occurs at high Reynolds numbers.

Answer

Laminar and turbulent flow can occur at any Reynolds number.

Answer

The Reynolds number is not related to the flow regime.

Question 2

Which of the following dimensionless groups characterizes the pressure drop in a pipe?

Accepted Answer

Friction factor

Answer

Reynolds number

Answer

Froude number

Answer

Weber number

Question 3

A 1:10 scale model of a ship is built. If the prototype ship has a speed of 20 knots, calculate the speed of the scale model to maintain dynamic similarity.

Accepted Answer

6.32 knots

Answer

2 knots

Answer

20 knots

Answer

63.2 knots

Question 4

How has dimensional analysis advanced the field of fluid mechanics?

Accepted Answer

By creating dimensionless numbers that describe fluid flow and heat transfer.

Accepted Answer

By allowing engineers to design and optimize fluid systems more efficiently.

Accepted Answer

By helping identify the most important factors affecting fluid flow and heat transfer.

Answer

By providing a universal set of equations for all fluid mechanics problems.

Question 5

Define the primary purpose of dimensional analysis.

Accepted Answer

Establishing physical relationships between variables

Answer

Simplifying fluid mechanics problems

Answer

Calculating specific fluid properties

Answer

Verifying experimental results

Question 6

According to the Buckingham Pi theorem, the number of dimensionless parameters required to describe a physical phenomenon is equal to:

Accepted Answer

The difference between the number of physical quantities and the number of fundamental dimensions

Answer

The number of fundamental dimensions

Answer

The number of physical quantities involved

Answer

The sum of the number of physical quantities and the number of fundamental dimensions

Question 7

Which of the following is NOT a fundamental dimension in the context of dimensional analysis?

Accepted Answer

Electrical charge

Answer

Mass

Answer

Force

Answer

Temperature

Question 8

Which dimensionless number is used to characterize fluid flow in a pipe, where viscous forces are dominant?

Accepted Answer

Reynolds number

Answer

Nusselt number

Answer

Schmidt number

Answer

Grashof number

Question 9

Which of the following is the correct equation for calculating the Reynolds number?

Accepted Answer

Re = ρVL/μ

Answer

Re = μVL/ρ

Answer

Re = VρL/μ

Answer

Re = VμL/ρ

Question 10

The Froude number characterizes:

Accepted Answer

Free surface flow

Answer

Incompressible fluid flow

Answer

Compressible fluid flow

Answer

Turbulent flow

Question 11

Which dimensionless group is used to characterize heat transfer by convection?

Accepted Answer

Nusselt number

Answer

Strouhal number

Answer

Weber number

Answer

Euler number

Question 12

What is the Buckingham Pi theorem primarily used for?

Accepted Answer

Determining the number of dimensionless groups in a system.

Answer

Calculating the values of dimensionless numbers.

Answer

Identifying key physical quantities involved in a problem.

Answer

Scaling experimental results.

Question 13

Which of the following is an example of a dimensionless group?

Accepted Answer

Reynolds number

Answer

Force

Answer

Velocity

Answer

Density

Question 14

What is the purpose of non-dimensionalizing governing equations in fluid mechanics?

Accepted Answer

Both (a) and (c).

Answer

To generalize equations for wider applicability to various systems.

Answer

To simplify equations for easier solving.

Answer

To eliminate the need for physical units in equations.

Question 15

Which of the following is a valid unit for pressure?

Accepted Answer

Pascal (Pa): the SI unit of pressure, defined as one newton per square meter.

Answer

Newton (N): the SI unit of force, not a unit of pressure.

Answer

Kilogram (kg): the SI unit of mass, not a unit of pressure.

Answer

Meter (m): the SI unit of length, not a unit of pressure.

Question 16

What is the main objective of non-dimensionalizing a governing equation?

Accepted Answer

To eliminate units and simplify the equation

Answer

To make the equation dimensionless

Answer

To increase the accuracy of the equation

Answer

To reduce the number of variables in the equation

Question 17

Which of the following is a limitation of dimensional analysis?

Accepted Answer

Inability to predict exact numerical values

Answer

Requirement for prior knowledge of all relevant physical variables

Answer

Applicability only to linear systems

Answer

Unreliability for complex problems

Question 18

How is the number of dimensionless numbers related to the number of fundamental dimensions?

Accepted Answer

One less than

Answer

Equal to

Answer

Twice as many

Answer

No relation

Question 19

Identify the non-fundamental dimension among the following:

Accepted Answer

Force

Answer

Mass

Answer

Length

Answer

Time

Question 20

According to the Buckingham Pi theorem, the number of dimensionless groups in a problem is equivalent to:

Accepted Answer

The number of physical quantities minus the number of fundamental dimensions

Answer

The number of fundamental dimensions

Answer

The number of variables

Answer

The number of equations

Question 21

The Reynolds number, a dimensionless number, primarily characterizes:

Accepted Answer

The ratio of inertial forces to viscous forces

Answer

The ratio of gravitational forces to inertial forces

Answer

The ratio of viscous forces to gravitational forces

Answer

The ratio of pressure forces to viscous forces

Question 22

Identify the primary limitation of dimensional analysis:

Accepted Answer

Inability to predict absolute values of physical quantities

Answer

Exclusively applicable to linear systems

Answer

Limited to incompressible fluids

Answer

Only applicable to steady-state systems

Question 23

The principle of similarity implies that:

Accepted Answer

Systems with similar geometry and identical dimensionless numbers exhibit similar behavior

Answer

Systems with identical dimensionless numbers display similar behavior

Answer

Systems with similar geometry demonstrate similar behavior

Answer

Systems with similar fluid properties exhibit similar behavior

Question 24

Which dimensionless number characterizes the ratio of inertial forces to viscous forces?

Accepted Answer

Reynolds number

Answer

Froude number

Answer

Weber number

Answer

Euler number