Heat Transfer Multiple Choice Questions & Answers (MCQs) on “Dimensional Homogeneity”.
1. How is dimensional homogeneity related with fundamental units of measurements?
a) Independent
b) Dependent
c) Dependent but can vary
d) Twice
Answer: a
Clarification: This implies that the length dimension can be added to subtract from only a length dimension.
2. What is the time period of oscillation of a simple pendulum of length L and mass m?
a) 2 π (L/g) 3/2
b) 2 π (L/g)
c) 2 π (L/g) 2
d) 2 π (L/g) 1/2
Answer: d
Clarification: The time period of a simple pendulum means the time it takes for one complete revolution.
3. The principle of dimensional homogeneity serves the following useful 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
a) i and ii
b) ii and iii
c) i, ii and iii
d) ii only
Answer: c
Clarification: It serves all the aspects.
4. The equation of friction loss in a pipe of length l and diameter d through which fluid flows with velocity v is
a) h i = 4 f V 2/d g
b) h i = 4 f V 2/d 2 g
c) h i = 4 f V 2/d 2 g
d) h i = 4 f V 2/2 g
Answer: b
Clarification: Here f is any constant with no dimensions whatsoever.
5. Bernoulli’s equation for fluid flow along a stream line is given as
a) p/w + V 2/2 g + y = 2
b) p/w + V/2 g + y = constant
c) p/w + V 2/2 g + y = 1
d) p/w + V 2/2 g + y = constant
Answer: d
Clarification: This is the Bernoulli’s equation and is dimensionally homogenous.
6. The convective film coefficient in k cal/m2 hr degree can be converted to J/m2 s degree by multiplying it with a factor
a) 1.1627
b) 1.1527
c) 1.1427
d) 1.1327
Answer: a
Clarification: Both k cal/m2 hr degree and J/m2 s are the units of convective film coefficient.
7. The pressure in kg/cm2 can be converted to N/m2 by multiplying it with a factor
a) 9.807 * 10 2
b) 9.807 * 10 3
c) 9.807 * 10 4
d) 9.807 * 10 5
Answer: c
Clarification: Both kg/cm2 and N/m2 are the units of pressure.
8. How many Newton’s are there in one kg?
a) 9.507
b) 9.607
c) 9.707
d) 9.807
Answer: d
Clarification: 1 kg = 9.807 N. Newton is the unit of force and kg is the unit of mass.
9. How many Joule are there in 1 k cal?
a) 3186
b) 4186
c) 5186
d) 6186
Answer: b
Clarification: 1 k cal = 4186 J. Joule is the unit of work done.
10. How many fundamental quantities are there?
a) 1
b) 2
c) 3
d) 4
Answer: c
Clarification: These are M, L and T. M is mass, L is length and T is time.