CLB 10904

CHEMICAL PROCESS PRINCIPLES

TUTORIAL 1B (Basic Concepts)

Dimension Homogeneity & Dimensionless Quantities

1. Which one of the following quantities is dimensionless?

a) 68o

b) sin (68o)

c) e68

d) Force

e) 6

f) Frequency

g) Log (0.0034)

2. Determine the dimensions of the following quantities.

a) Volume

b) Acceleration (velocity/time)

c) Density (mass/volume)

d) Force (mass x acceleration)

3. What are the dimensions of the following?

a) 3

b) Height

c) Frequency

d) Area x volume

e) Displacement

f) 0.5 x volume

4. Determine if the following equations are dimensionally correct.

a)

Where:

X is the displacement at time t

Xo is the displacement at time t=0

Vo is the velocity at time t=0

a is the constant acceleration

b)

Where:

Nd and Na are number of particles

V is volume

g is gravitational acceleration

hd is distance

is density

k is Boltzmans constant with SI units (J/K)

T is absolute temperature

c) E = mc2

Where:

E is energy (J)

m is mass

c is speed of light

5. Explain in detail whether the following equation for flow through a rectangular weir is

dimensionally consistent.

0.415" # 0.2%&%.'(2)

Where:

q is volumetric flowrate, ft3/s

L is crest height, ft

ho is weir head, ft

g is acceleration gravity, 32.2 ft/s2

6. Consider the equation

D (ft) = 3t(s) + 4

a) If the equation is valid, what are the dimensions of the constant 3 and 4?

b) If the equation is consistent in its unit, what are the units of 3 and 4?

c) Derive an equation for distance in meters in terms of time in minutes.