# Food Processing Unit Operations Questions and Answers – Unit Systems – Dimensional Analysis

This set of Food Processing Unit Operations Interview Questions and Answers focuses on “Unit Systems – Dimensional Analysis”.

1. The analytical procedure of studying physical phenomena in variables, and corelating them to obtain a dimensionless group is known as ________
a) Dimensional constants
b) Dimensional homogeneity
c) Dimensional variable
d) Dimensional analysis

Explanation: The study of variables corelated to their physical phenomena and studying them analytically to solve problems refers to Dimensional analysis. If the equation expresses a proper relationship between the both, then dimensional homogeneity is obtained and the varying quantities are called dimensional variables, whereas the values normally held constant, are called dimensional constants.

2.The occurrence of closeness of measured values towards each other is known as ______
a) Accuracy
b) Precision
c) Measurement
d) Dimensional Analysis

Explanation: Precision is the closeness of more than one values towards each other. On the other hand, Accuracy is the closeness of the measured value to the known or standard value.

3. What are the principles for ensuring the consistency of an equation through dimensional analysis?
Statement I: The sum of all exponents of any dimension (e.g., mass), should be the same on both sides of the equation.
Statement II: An exponent must itself be a pure / dimensionless number.
Statements III: The magnitude of the exponent does not necessarily have to be a whole number.
a) I & II
b) II
c) III
d) I, II & III

Explanation: To verify the correctness of any given equation through dimensional analysis, we need to ensure that the sums of all exponents relating to any given dimension are equal on both sides of the equation. The exponent should be dimensionless or in other words, a pure number, although its magnitude does not necessarily have to be a whole number.

4. State True or False.
Statement I: Through dimensional analysis of Physical quantities we can verify whether an equation is correct or not.
Statement II: With dimensional analysis we can derive a relation between various physical quantities.
a) True, True
b) False, False
c) True, False
d) False, True

Explanation: The main purpose of using dimensional analysis, is to verify whether a given equation is correct or not. It also assists the derivation of a relationship between various physical quantities.

5. What are the dimensions of Energy?
a) (MLT-2)
b) (M-1L3T-2)
c) (M L2T-2)
d) (LT-2)

Explanation: Energy is also known as work done, for which the formula is the product of force into displacement, i.e. Work = Force (mass x acceleration) X Displacement (in meters). We know that the dimensions for force and displacement are (MLT-2) and (L) respectively. Therefore, the dimensions for Energy are (M L2T-2).
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6. In Fluid dynamics, Reynold’s number is a dimensionless number. True or False?
a) False
b) True

Explanation: In fluid dynamics, inertial forces are very important and the ratio of these inertial forces to viscous, pressure, gravity, surface tension and compressibility forces lead to formation of fundamental dimensionless groups. Reynold’s number is the ratio of inertial force to viscous force and is thus, dimensionless.

7. What is the ratio of inertial force to gravitational force known as?
a) Weber number
b) Froude number
c) Reynold’s number
d) Euler Number

Explanation: Fr or Froude number is the ratio of inertial force to gravitational force. Its formula is Fr =$$\frac{V}{\sqrt{g.L}}$$ . On the other hand, Weber number is the ratio of inertial force to surface tension and Reynold’s number is the ratio of inertial force to viscous force.

8. Which dimensionless number is denoted by the equation Pr =$$\frac{μC_p}{k}$$ ?
a) Prandtl number
b) Weber number
c) Reynold’s number
d) Froude number

Explanation: Prandtl number is a dimensionless number used to determine heat convection. It is the ratio of the amount of heat dissipated to the amount of heat conducted. Whereas, Froude number is the ratio of inertial force to gravitational force, Weber number is the ratio of inertial force to surface tension and Reynold’s number is the ratio of inertial force to viscous force.

9. Is Plane angle a derived unit?
a) True
b) False

Explanation: There are seven basic or standard units. Plane angle is one of them, like Mass, Length, Time, etc. It is measured in radians and denoted by ‘rad’.

10. What is the ratio of inertial force to compressibility force and is also the key parameter, characterizing compressibility effects in fluids?
a) Froude number
b) Strouhal number
c) Mach number
d) Weber number

Explanation: Mach number (M) is the ratio of inertial force to compressibility force and is used in problems where fluid compressibility is important. Strouhal number, on the other hand, is important in unsteady, oscillating flow problems. Froude number is the ratio of inertial force to gravitational force whereas, Weber number is the ratio of inertial force to surface tension.

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