FLUID MECHANICS
FOR
CHEMICAL ENGINEERS
Introduction
Fluid mechanics, a special branch of general mechanics, describes the laws of
liquid and gas motion. Flows of liquids and gases play an important role in
nature and in technical applications, as, for example, flows in living
organisms, atmospheric circulation, oceanic currents, flows in rivers, windand water loads on buildings and structures, gas motion in flames and
explosions, aero- and hydrodynamic forces acting on airplanes and ships,
flows in water and gas turbines, pumps, engines, pipes, valves, bearings,
hydraulic systems, and others. The Fluid Mechanics is essential in Chemical
Engineering because the majority of chemical –processing operations are
conducted either partly or totally in the fluid phase. Examples of such
operations abound in the Biochemical, chemical, energy, fermentation,
materials, petroleum, pharmaceutical, polymers and waste-processing
industries.
So what is a Fluid?
A fluid is defined as a substance that deforms continuously whilst acted upon
by any force tangential to the area on which it acts. Such a force is termed a
shear force, and the ratio of the shear force to the area on which it acts is
known as the shear stress.
The rate at which the fluid deforms continuously depends not only on the
magnitude of the applied force but also on a property of the fluid called its
viscosity or resistance to deformation and flow.
• Pressure
Force per unit area is called pressure, and its
unit is the Pascal, N/m2 in the SI system and
psia, lbf/in2 absolute, in the English system.
Force F
P

Area
A
N
1 kPa  10
m2
6 N
3
1 MPa  10

10
kPa
2
m
3
• The pressure used in all calculations of state is the
absolute pressure measured relative to absolute
zero pressure.
However, pressures are often
measured relative to atmospheric pressure called
gage or vacuum pressures. In the English system
the absolute pressure and gage pressures are
distinguished by their units, psia (pounds force per
square inch absolute) and psig (pounds force per
square inch gage), respectively; however, the SI
system makes no distinction between absolute and
gage pressures.
Pgage  Pabs  Patm
Pvac  Patm  Pabs
Pabs  Patm  Pgage
The relation among atmospheric, gage, and vacuum pressures is shown below. Small to
moderate pressure differences are measured by a manometer and a differential fluid
column of height h corresponds to a pressure difference between the system and the
surroundings of the manometer. This pressure difference is determined from the
manometer fluid displaced height as
Velocity
• If the fluid passes through a plane of area A
normal to the direction of the velocity,, the
corresponding volumetric flow rate of fluid
through the plane is Q =u A.
• The corresponding mass flow rate is m= p Q = p
u A, where p is the (constant) fluid density.
• When velocity is multiplied by mass it gives
momentum, a quantity of prime importance in
fluid mechanics. The corresponding momentum
flow rate passing through the area A is M = mu
= p u2 A.
Basic laws.
• When applying these laws, the procedure is
first to identify a system, its boundary, and its
surroundings; and second, to identify how the
system interacts with its surroundings. Refer to
Fig. and let the quantity X represent either
mass, energy, or momentum.
Density
• S= p/ pw
• Degrees A.P.I. (American Petroleum
Institute) are related to specific gravity s by
the formula
A.P.I= 141.5/S -131.5
Thus, for the crude oil listed in Table 1.1,
indeed gives 141.5/0.851 — 131.5 =
35°A.P.I.
• Densities of gases. For ideal gases, pV nRT,
where p is the absolute pressure, V is the
volume of the gas, n is the number of moles,
R is the gas constant, and T is the absolute
temperature. If M is the molecular weight of
the gas, it follows that:
p= PM/RT
• For NON ideal gases
p= PM/ZRT
VISCOSITY
All fluids offer resistance to any force tending to
cause one layer to move over another. Viscosity
is the fluid property responsible for this
resistance. Since relative motion between layers
requires the application of shearing forces, that
is, forces parallel to the surfaces over which they
act, the resisting forces must be in exactly the
opposite direction to the applied shear forces
and so they too are parallel to the surfaces.
SURFACE TENSION
Surface tension arises from the forces
between the molecules of a liquid and the
forces (generally of a different magnitude)
between the liquid molecules and those of
any adjacent substance.
Units
An important component to the solution to any
engineering thermodynamic problem requires the
proper use of units.