The pharmaceutical scientist is familiar with the units (dimensions) of centi-meter (length), gram (mass), and second (time) or the conventional Syste`me Internationale (SI) units of meter, kilogram, and second.

**Pharmaceutical Process Engineering**

**Units and Dimensions**

The
pharmaceutical scientist is familiar with the units (dimensions) of centi-meter
(length), gram (mass), and second (time) or the conventional Syste`me
Internationale (SI) units of meter, kilogram, and second. The engineer, in contrast,
will express equations and calculations in units that suit quantities he or she
is measuring. To reconcile in part this disparity, a brief account of units and
dimensions follows.

Mass
(M), length (L), time (T), and temperature (°) are four of six funda-mental
dimensions, the units of which have been fixed arbitrarily and from which all
other units are derived. The fundamental units adopted for this book are the
kilogram (kg), meter (m), second (sec), and Kelvin (K). The derived units are
frequently self-evident. Examples are area (m^{2}) and velocity
(m/sec). Others are derived from established laws of physics. Thus, a unit of
force can be obtained from the law that relates force, *F*, to mass, *m*, and
acceleration, *a*:

F
= *kma*

where
*k* is a constant. If we choose our
unit of force to be unity when the mass and acceleration are each unity, the
units are consistent. On this basis, the unit of force is Newton (N). This is
the force that will accelerate a kilogram mass at 1 m/sec.

Similarly,
a consistent expression of pressure [i.e., force per unit area is Newtons per
square meter (N/m^{2} or Pascal, Pa)]. This expression exemplifies the
use of multiples or fractions of the fundamental units to give derived units of
practical importance. A second example is dynamic viscosity [M/(L·T)] when the
consistent unit kg/(m·sec), which is enormous, is replaced by kg/(m·hr) or even
by poise. Basic calculations using these quantities must then include
conversion factors.

The
relationship between weight and mass causes confusion. A body falling freely
due to its weight accelerates at kg·m/sec^{2} (g varies with height and
latitude). Substituting k =
1 in the preceding equation gives W = mg, where W is the weight of the
body (in Newtons). The weight of a body has dimensions of force, and the mass
of the body is given by

mass(kg) = weight (N) / *g*(m/sec^{2})

The
weight of a body varies with location; the mass does not. Problems arise when,
as in many texts, kilogram is a unit of mass and weight of a kilogram is the
unit of force. For example, an equation describing pressure drop in a pipe is

ΔP = 32*ul*η /*d*^{2}

when
written in consistent units—ΔP
as N/m^{2}, viscosity (η)
as kg/(m·sec), velocity (*u*) as m/sec,
distance (*l*) as m, and tube diameter
(*d*) as m. However, if the kilogram
force is used (i.e., pressure is measured in kg/m^{2}), the equation
must be

ΔP = 32*ul*η /*d*^{2}

where
g = 9.8 m/sec^{2}.
In tests using this convention, the conversion factor *g* appears in many equations.

The
units of mass, length, and time commonly used in engineering heat transfer are
kilogram, meter, and second, respectively. Temperature, which is a fourth
fundamental unit, is measured in Kelvin (K). The unit of heat is the Joule (J),
which is the quantity of heat required to raise the temperature of 1 g of water
by 1 K. Therefore, the rate of heat flow, Q, often referred to as the total
heat flux, is measured in J/sec. The units of thermal conductivity are J/(m^{2}·sec·K/m).
This may also be written as J/(m·sec·K), although this form is less expressive
of the meaning of thermal conductivity.

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