Methods of Dimensional Analysis Associated with Heat Transfer

This quiz contains multiple-choice problems on dimensional systems and homogeneity, Rayleigh and Buckingham methods, model simulation and studies, the importance of dimensionless groups and the advantages and disadvantages of dimensional analysis.

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How many fundamental quantities are there?

1 2 3 4

Which of the following is not known as a core group?

Time Geometric property Fluid property Flow characteristics

If there are 6 physical quantities and 3 fundamental units, then the number of pi terms are

1 2 3 4

The study of predicting prototype conditions from model observations is known as

Similitude Geometrical similarity Prototype Model

The principle of dimensional homogeneity serves the following practical concepts:
(i) It helps to check whether an equation of any physical phenomenon is dimensionally homogenous or not
(ii) It helps to determine the dimensions of a physical quantity
(iii) It helps to convert the units from one system to another
Identify the correct statements.

i and ii

ii and iii

i, ii and iii

ii only

How is dimensional homogeneity related to fundamental units of measurements?

Independent

Dependent

Dependent but can vary

Twice

The S.I unit of heat is

J-s

W/K

Bernoulli’s equation for fluid flow along a streamline is given as

p/w + (V^2)/2 g + y = 2

p/w + V/2 g + y = constant

p/w + (V^2)/2 g + y = 1

p/w + (V^2)/2 g + y = constant

The convective film coefficient in k cal/m^2 hr degree can be converted to J/m^n2 s degree by multiplying it with a factor

1.1627

1.1527

1.1427

1.1327

The pressure in kg/cm^2 can be converted to N/m^2 by multiplying it with a factor

9.807 * 10^2

9.807 * 10^3

9.807 * 10^4

9.807 * 10^5

How much force is exerted by a body of 1 kg on the ground whilst under freefall?

9.507

9.607

9.707

9.807

How many joules makeup one kcal?

3186

4186

5186

6186

If there are n variables in a dimensionally homogeneous equation and these variables contain m primary dimensions, then the variables can be grouped into how many non-dimensional parameters?

n - m

n - 2*m

What is the time period of oscillation of a simple pendulum having length L and mass m?

2*π*(L/g)^(3/2)

2*π*(L/g)

2*π*(L/g)^2

2*π*(L/g)^(1/2)

The equation of friction loss in a pipe of length l and diameter d through which fluid flows with velocity v is

h{i} = 4*f*(V^2)/d*g

h{i} = 4*f*(V^2)/2*d*g

h{i} = 4*f*(V^2)/2*d

h{i} = 4*f*(V^2)/2*g