Dimensional Analysis in Fluid Mechanics: Master Engineering Concepts

Question 1

Enhanced clarity: The Buckingham Pi theorem states that the number of dimensionless groups 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

Answer

The number of variables multiplied by the number of fundamental dimensions

Answer

The number of variables divided by the number of fundamental dimensions

Question 2

Corrected answer: Which of the following is a limitation of dimensional analysis?

Accepted Answer

It cannot account for all physical effects **in all scenarios**

Answer

It cannot provide numerical solutions

Answer

It is only applicable to linear systems

Answer

It requires a complete understanding of the problem

Question 3

Corrected Question: Dimensional analysis is based on the principle of:

Accepted Answer

Dimensional homogeneity

Answer

Dimensional independence

Answer

Dimensional invariance

Answer

Dimensional equivalence

Question 4

The Reynolds number is a dimensionless parameter that characterizes the ratio of:

Accepted Answer

Inertial forces to viscous forces

Answer

Pressure forces to viscous forces

Answer

Gravitational forces to inertial forces

Answer

Elastic forces to viscous forces

Question 5

Which of the following is a valid Buckingham Pi theorem equation?

Accepted Answer

$f(\pi_1, \pi_2) = 0$

Answer

$g(\pi_1, \pi_2, \pi_3) = 0$

Answer

$h(\pi_1, \pi_2, \pi_3, \pi_4) = 0$

Answer

$\pi_1 + \pi_2 + \pi_3 = 0$

Question 6

Which of the following is NOT a base quantity in physics?

Accepted Answer

Velocity

Answer

Mass

Answer

Time

Question 7

Which of the following statements correctly describes the Buckingham Pi theorem?

Accepted Answer

The number of dimensionless groups is equal to the number of variables minus the number of fundamental dimensions.

Answer

The number of dimensionless groups is equal to the number of variables plus the number of fundamental dimensions.

Answer

The number of dimensionless groups is equal to the square of the number of fundamental dimensions.

Question 8

In fluid mechanics, what is the primary purpose of dimensional analysis?

Accepted Answer

To reduce the number of variables in a problem by grouping them into dimensionless parameters.

Answer

To solve differential equations governing fluid flow.

Answer

To determine the physical properties of fluids.

Question 9

Which dimensionless group represents the ratio of inertial forces to viscous forces in fluid mechanics?

Accepted Answer

Reynolds number

Answer

Mach number

Answer

Froude number

Answer

Grashof number

Question 10

What is the primary significance of the similarity parameter in dimensional analysis?

Accepted Answer

It ensures that the dimensionless groups are identical for both the model and the prototype.

Answer

It determines the scale factor between the model and the prototype.

Answer

It provides a measure of the accuracy of the model.

Question 11

What is the main advantage of utilizing dimensional analysis in fluid mechanics?

Accepted Answer

It provides valuable insights into the physical behavior of fluids and simplifies problem-solving.

Answer

It guarantees precise predictions of fluid flow.

Answer

It eliminates the need for experimental testing.

Question 12

What is a primary limitation of dimensional analysis in fluid mechanics?

Accepted Answer

It cannot predict exact values of fluid properties or flow parameters.

Answer

It is only applicable to incompressible fluids.

Answer

It requires a complete understanding of the governing equations.

Question 13

Identify the correct sequence of steps involved in performing dimensional analysis.

Accepted Answer

Identify variables, choose repeating variables, form dimensionless groups, and interpret results.

Answer

Define boundary conditions, solve differential equations, and visualize results.

Answer

Derive governing equations, conduct experiments, analyze data, and draw conclusions.

Question 14

The pressure drop in a pipe is given by the Darcy-Weisbach equation: Δp = f * (L/D) * (V^2 / 2g). What are the dimensions of the friction factor, f?

Accepted Answer

Dimensionless

Answer

Time

Answer

Mass

Answer

Length

Question 15

Which of the following is an example of a derived dimension?

Accepted Answer

Area

Answer

Length

Answer

Mass

Question 16

The Buckingham Pi theorem states that:

Accepted Answer

The number of dimensionless groups is equal to the number of variables minus the number of fundamental dimensions in the system.

Answer

Dimensionless groups can be formed by combining any set of variables.

Question 17

The Froude number is used to characterize:

Accepted Answer

Flow similarity in open channels

Answer

Boundary layer flow

Answer

Pipe flow

Answer

Turbulent flow

Question 18

Which of the following is NOT a fundamental dimension in the International System of Units (SI)?

Accepted Answer

Energy

Answer

Time

Answer

Length

Answer

Mass

Question 19

The Buckingham Pi theorem states that the number of dimensionless groups that can be formed from a set of variables is equal to:

Accepted Answer

The number of variables minus the number of fundamental dimensions.

Answer

The number of variables.

Answer

The number of fundamental dimensions.

Question 20

A dimensionless group formed from the variables density (ρ), velocity (V), and viscosity (μ) is:

Accepted Answer

Reynolds number (Re)

Answer

Mach number (M)

Answer

Froude number (Fr)

Question 21

A model of a ship is built to a scale of 1:50. If the prototype ship has a length of 100 meters, what is the length of the model?

Accepted Answer

2 meters

Answer

0.5 meters

Answer

5 meters

Answer

50 meters

Question 22

Which of the following statements about dimensional analysis is TRUE?

Accepted Answer

Dimensional analysis can be used to determine the functional relationship between variables, but it cannot determine the exact constants in the relationship.

Answer

Dimensional analysis can determine both the functional relationship and the exact constants in the relationship.

Question 23

The Froude number is a dimensionless group that represents the ratio of:

Accepted Answer

Inertia forces to gravity forces

Answer

Surface tension forces to inertia forces

Answer

Elastic forces to inertia forces

Answer

Viscous forces to inertia forces

Question 24

In a wind tunnel experiment, the model is designed to have a Reynolds number equal to the Reynolds number of the prototype. This is an example of:

Accepted Answer

Dynamic similarity

Answer

Kinematic similarity

Answer

Geometric similarity

Answer

Thermal similarity

Question 25

A researcher is studying the flow of water through a pipe. They want to use dimensional analysis to determine the relationship between the flow rate (Q), pipe diameter (D), and fluid viscosity (μ). Which of the following dimensionless groups is relevant to this problem?

Accepted Answer

Reynolds number (Re) and friction factor (f)

Answer

Weber number (We) and Euler number (Eu)

Answer

Froude number (Fr) and Mach number (M)

Question 26

A student is asked to design a model of a dam to study the forces acting on it. The prototype dam has a height of 100 meters. The student decides to build a model with a height of 1 meter. What is the scale of the model?

Accepted Answer

1:100

Answer

10:1

Answer

100:1

Answer

1:10