Dimensional Analysis and Similitude: Master Fluid Systems with Ease

Question 1

Which of the following is **not** a dimensionless number commonly used in engineering?

Accepted Answer

Specific gravity

Answer

Reynolds number

Answer

Froude number

Answer

Mach number

Question 2

The Reynolds number is a dimensionless parameter that characterizes:

Accepted Answer

The ratio of inertial forces to viscous forces

Answer

The ratio of gravitational forces to viscous forces

Answer

The ratio of pressure forces to viscous forces

Answer

The ratio of surface tension forces to viscous forces

Question 3

The Froude number is a dimensionless parameter that characterizes:

Accepted Answer

The ratio of inertial forces to gravitational forces

Answer

The ratio of viscous forces to gravitational forces

Answer

The ratio of pressure forces to gravitational forces

Answer

The ratio of surface tension forces to gravitational forces

Question 4

The Mach number is a dimensionless parameter that is defined as the ratio of:

Accepted Answer

The velocity of a fluid to the speed of sound

Answer

The pressure of a fluid to the atmospheric pressure

Answer

The temperature of a fluid to the boiling point

Answer

The density of a fluid to the water density

Question 5

The Grashof number is a dimensionless parameter that characterizes:

Accepted Answer

The ratio of buoyancy forces to viscous forces

Answer

The ratio of inertial forces to viscous forces

Answer

The ratio of pressure forces to viscous forces

Answer

The ratio of surface tension forces to viscous forces

Question 6

Which of the following is the most accurate representation of the Buckingham Pi theorem?

Accepted Answer

Π₁ = f(Π₂, Π₃, ..., Πₙ)

Answer

Π₁ = f(Π₂, Π₃, ..., Πₘ)

Answer

Π₁ = f(Π₂, Π₃, ..., Πₙ, m)

Answer

Π₁ = f(Π₂, Π₃, ..., Πₙ, n)

Question 7

A scaled model of a bridge is built at a scale of 1:100. If the velocity of wind in the prototype is 15 m/s, what should be the velocity of wind in the model to ensure dynamic similarity?

Accepted Answer

0.15 m/s

Answer

1.5 m/s

Answer

15 m/s

Answer

150 m/s

Question 8

Which of the following dimensionless numbers is used to characterize the behavior of a fluid flowing through a pipe?

Accepted Answer

Reynolds number

Answer

Froude number

Answer

Mach number

Answer

Strouhal number

Question 9

According to the Buckingham Pi theorem, the number of dimensionless groups (Π) is expressed as:

Accepted Answer

Π = Number of variables (n) - Number of fundamental dimensions (k)

Answer

Π = n + k

Answer

Π = n / k

Answer

Π = (n - k) * k

Question 10

The systematic process of determining the dimensionless groups for a given problem is known as:

Accepted Answer

Dimensional analysis

Answer

Dimensional similitude

Answer

Scale modeling

Answer

Prototype testing

Question 11

Which of the following requirements is NOT essential for dimensional similitude?

Accepted Answer

Material similarity

Answer

Geometric similarity

Answer

Kinematic similarity

Answer

Dynamic similarity

Question 12

The Reynolds number is primarily used to analyze:

Accepted Answer

Laminar and turbulent flow

Answer

Incompressible flow in pipes

Answer

Boundary layer thickness

Answer

Heat transfer in fluids

Question 13

According to the Buckingham Pi theorem, the number of dimensionless parameters in a problem is equal to:

Accepted Answer

The number of independent variables minus the number of fundamental dimensions

Answer

The number of dependent variables plus the number of fundamental dimensions

Answer

The number of independent variables plus the number of fundamental dimensions

Answer

The number of dependent variables minus the number of fundamental dimensions

Question 14

Which of the following is NOT a fundamental dimension in mechanics?

Accepted Answer

Temperature

Answer

Mass

Answer

Time

Answer

Length

Question 15

The model fluid most commonly used in wind tunnel testing is:

Accepted Answer

Air

Answer

Water

Answer

Glycerin

Answer

Mercury

Question 16

The ratio of inertial forces to viscous forces in a fluid flow is represented by:

Accepted Answer

Reynolds number

Answer

Mach number

Answer

Froude number

Answer

Euler number

Question 17

The dimensionless parameter Mach number is used to characterize:

Accepted Answer

Compressible flow

Answer

Viscous flow

Answer

Turbulent flow

Answer

Laminar flow

Question 18

Which of the following is a limitation of using dimensional analysis and similitude?

Accepted Answer

It assumes that the governing equations are known

Answer

It only applies to incompressible fluids

Answer

It is only valid for small-scale systems

Answer

It requires complex mathematical analysis

Question 19

The process of non-dimensionalizing a governing equation involves:

Accepted Answer

Dividing the equation by a characteristic value

Answer

Multiplying the equation by a characteristic value

Answer

Subtracting a characteristic value from the equation

Answer

Adding a characteristic value to the equation

Question 20

The dimensionless parameter Weber number is used to characterize:

Accepted Answer

Free surface flows

Answer

Viscous flows

Answer

Compressible flows

Answer

Turbulent flows

Question 21

According to the Buckingham Pi theorem, the number of dimensionless parameters needed to describe a system is equal to:

Accepted Answer

the difference between the number of primary variables and the number of fundamental dimensions

Answer

the number of primary variables in the system

Answer

the number of fundamental dimensions in the system

Answer

the number of independent variables in the system

Question 22

Which of the following is NOT a fundamental dimension in the SI system?

Accepted Answer

force

Answer

mass

Answer

length

Answer

time

Question 23

The dimensionless number that represents the ratio of inertial forces to viscous forces is:

Accepted Answer

Reynolds number

Answer

Weber number

Answer

Froude number

Answer

Euler number

Question 24

Similitude between two systems implies that:

Accepted Answer

they have the same dimensionless numbers

Answer

they have the same shape

Answer

they are made of the same material

Answer

they have the same mass

Question 25

Which of the following is an example of a prototype in the context of similitude?

Accepted Answer

a full-scale version of a ship

Answer

a scaled-down model of an aircraft

Answer

a computer simulation of a fluid system

Answer

a mathematical equation representing a fluid flow

Question 26

The Reynolds number is used primarily to determine:

Accepted Answer

the likelihood of laminar or turbulent flow

Answer

the drag force on a body

Answer

the heat transfer rate from a surface

Answer

the pressure drop in a pipe

Question 27

Which of the following dimensionless numbers is used to characterize the behavior of a fluid in a gravitational field?

Accepted Answer

Froude number

Answer

Weber number

Answer

Mach number

Answer

Nusselt number

Question 28

The process of converting a system to a dimensionless form is known as:

Accepted Answer

non-dimensionalization

Answer

scaling

Answer

normalization

Answer

simplification

Question 29

Which of the following assumptions is NOT made in the Buckingham Pi theorem?

Accepted Answer

the system is linear

Answer

the variables are independent

Answer

the functional relationship between variables is known

Answer

the dimensions are consistent

Question 30

The Weber number is a dimensionless number that represents the ratio of:

Accepted Answer

inertial forces to surface tension forces

Answer

inertial forces to viscous forces

Answer

viscous forces to surface tension forces

Answer

gravitational forces to inertial forces

Question 31

How do the applications of dimensionless numbers differ when characterizing the behavior of liquids and gases?

Accepted Answer

The application of dimensionless numbers varies for liquids and gases due to their distinct physical properties and governing equations.

Answer

Dimensionless numbers are applied identically for both liquids and gases.

Answer

Dimensionless numbers are more applicable to liquids than gases.

Question 32

Which of the following is NOT a fundamental dimension in engineering mechanics, used to describe physical quantities?

Accepted Answer

Force

Answer

Mass

Answer

Length

Answer

Time

Question 33

Reynolds number, a dimensionless number, is used to characterize:

Accepted Answer

Fluid flow in pipes and channels

Answer

Heat transfer in fluids

Question 34

Which of the following is NOT an advantage of using dimensionless numbers in engineering analysis?

Accepted Answer

Predicts numerical values of physical quantities

Answer

Simplifies complex equations

Answer

Helps identify important parameters

Question 35

The Froude number is used to characterize:

Accepted Answer

Open-channel flow and the formation of hydraulic jumps

Answer

Compressible fluid flow

Question 36

The Mach number is used to characterize:

Accepted Answer

Compressible fluid flow and the effects of compressibility

Answer

Fluid flow in porous media

Question 37

Which of the following is a key assumption of dimensional analysis?

Accepted Answer

The physical laws governing the system are the same for all systems

Answer

The system is in equilibrium

Question 38

Identify the option that is NOT considered a fundamental dimension:

Accepted Answer

Acceleration

Answer

Mass

Answer

Length

Answer

Time

Question 39

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

Accepted Answer

Drag coefficient

Answer

Force

Answer

Energy

Answer

Volume

Question 40

Dimensional analysis involves the process of:

Accepted Answer

Simplifying a physical problem into a dimensionless form

Answer

Scaling a system based on geometric similarity

Answer

Predicting the exact values of physical quantities

Answer

Determining the dynamic similarity between two systems

Question 41

The Reynolds number is a dimensionless number that characterizes:

Accepted Answer

Flow behavior

Answer

Pressure drop

Answer

Heat transfer rate

Answer

Fluid density

Question 42

The process of designing a fluid mechanics system that behaves similarly to an existing system using dimensionless numbers is called:

Accepted Answer

Scaling

Answer

Model testing

Answer

Prototyping

Answer

Simulation

Question 43

Which of the following is the initial step in applying the Buckingham Pi theorem?

Accepted Answer

Identifying the relevant variables and their dimensions

Answer

Defining the dependent and independent variables

Answer

Guessing a set of dimensionless groups

Answer

Writing the governing equation in terms of dimensionless groups

Question 44

In the context of fluid flow through a pipe, which of the following is the most appropriate dimensionless group to consider?

Accepted Answer

Reynolds number

Answer

Strouhal number

Answer

Weber number

Answer

Eötvös number

Question 45

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

Accepted Answer

The difference between the number of variables and the number of fundamental dimensions

Answer

The sum of the number of independent and dependent variables

Answer

The ratio of the number of variables to the number of fundamental dimensions

Answer

The difference between the number of independent and dependent variables

Question 46

Similitude, as applied in fluid mechanics, primarily involves the study of:

Accepted Answer

Dynamically similar systems

Answer

Physically similar systems

Answer

Geometrically similar systems

Answer

Thermally similar systems

Question 47

Model testing, based on the principles of similitude, offers several advantages. Which of the following is NOT an advantage?

Accepted Answer

Elimination of all sources of error

Answer

Cost-effectiveness compared to full-scale testing

Answer

Controlled testing environment

Answer

Detailed insights into complex fluid flow phenomena

Question 48

Which of the following similarity criteria is used to ensure that the forces acting on a fluid system are similar?

Accepted Answer

Dynamic similarity

Answer

Geometric similarity

Answer

Kinematic similarity

Answer

Thermal similarity

Question 49

Which of the following is **NOT** a benefit of using dimensional analysis and similitude?

Accepted Answer

Elimination of the need for physical models

Answer

Reduced experimental testing

Answer

Improved understanding of fluid systems

Answer

Design optimization

Question 50

The Reynolds number is a dimensionless number that characterizes the ratio of inertial forces to viscous forces in a fluid flow. Its formula is:

Accepted Answer

ρVL/μ

Answer

μVL/ρ

Answer

ρVμ/L

Answer

LμV/ρ

Question 51

The Reynolds number represents the ratio of which two types of forces?

Accepted Answer

Inertial and viscous

Answer

Viscous and gravitational

Answer

Gravitational and elastic

Answer

Elastic and surface tension

Question 52

Consider a fluid flowing through a pipe with diameter D and velocity V. Which of the following dimensionless groups best characterizes the flow pattern?

Accepted Answer

ρDV/μ

Answer

DV/ρ

Answer

ρV²/D

Answer

μV/D

Question 53

The Froude number compares which two types of forces?

Accepted Answer

Inertial and gravitational

Answer

Viscous and pressure

Answer

Surface tension and inertial

Answer

Elastic and viscous

Question 54

Which of the following is a key assumption of the Buckingham Pi theorem?

Accepted Answer

The number of fundamental dimensions is greater than the number of variables

Answer

The governing equations are nonlinear

Answer

The system is not in equilibrium

Answer

The system is adiabatic

Question 55

Consider a projectile launched with velocity V and angle θ. Which dimensionless group is relevant for characterizing the trajectory?

Accepted Answer

V/√gL

Answer

V²/gL

Answer

V√g/L

Answer

V/L

Question 56

The Weber number compares which two types of forces?

Accepted Answer

Inertial and surface tension

Answer

Viscous and surface tension

Answer

Elastic and surface tension

Answer

Pressure and surface tension

Question 57

Which of the following is the most precise definition of a dimensionless number?

Accepted Answer

A quantity that is independent of all units

Answer

A quantity that has units of time only

Answer

A quantity that has units of mass only

Answer

A quantity that has units of length only

Question 58

What is the primary purpose of applying the Buckingham Pi theorem?

Accepted Answer

To reduce the number of variables required to describe a physical system

Answer

To find the solution to a complex mathematical equation

Answer

To convert units between different systems of measurement

Answer

To determine the scaling factors for a physical model

Question 59

Which of the following is NOT a type of commonly used dimensionless number?

Accepted Answer

Euler number

Answer

Reynolds number

Answer

Froude number

Answer

Mach number