3
Fluid Flow
3.1 Introduction
The term fluid applies to any material that has the ability to move of its own accord, even if that
movement is very slow. Therefore, gases, liquids, slurries and even some materials that you would
probably classify as solids – eg glass – are fluids.
Materials are usually transferred within a chemical plant in the fluid state, by pumping through
a network of pipes. In process design and analysis, it is necessary to determine many factors which
are dictated by fluid properties, especially those of fluid dynamics – the science of fluids in motion.
Some of these factors are:
•
pump size
•
pipe diameter
•
flow rate
•
viscosity/temperature profiles
3.2 Flow types
You might imagine that a liquid flowing through a pipe all flows through together, but this is not the
case. The pattern of flow which develops is dependent on a number of factors:
•
diameter of the pipe
•
velocity of the liquid
•
viscosity of the liquid
•
density of the liquid
The relationship between these four variables is shown in Equation 3.1, and is known as the Reynolds
equation after the physicist who conducted the key experiments on fluid flow.
Re =
vdρ
µ
Eqn 3.1
where Re is the Reynolds number (a value describing the type of flow), v the flow velocity in m/s, d
the pipe diameter (m), ρ the density (kg/m3) and µ the viscosity of the liquid (Pascal seconds).
CLASS EXERCISE 3.1
(a) A liquid of 125 mPa.s and density 800 g/L is pumped through a 20 cm diameter pipe at
a flow rate of 5.2 m/s. What is the Reynolds number?
(b)
What is the maximum flow rate if a liquid of viscosity 50 Pa.s and density 1.5 g/mL is
pumped through a 10 cm pipe, keeping the Reynolds Number to a below 2000?
3. Fluid Flow
MEASURES OF FLOW RATE – VOLUMETRIC VS AVERAGE VELOCITY
The units for v in the Reynolds equation are in m/s, but if you think about this, it is not the units that
you would normally expect to measure the flow rate of liquids: this would be by volume per unit time,
eg L/min – the volumetric flow rate. How can you convert from one to the other?
It is actually quite simple: the two values are related by the cross-sectional area of the pipe
through which the liquid is flowing, as shown in Equation 3.2. The velocity is the rate at which a
molecule of the fluid moves from point A to B, while the volumetric flow rate measures all the
molecules as they pass point A.
f=Av
Eqn 3.2
where f is the volumetric flow rate in m3/s, A the cross section area in m2 and v the velocity in m/s.
CLASS EXERCISE 3.3
(a) Calculate the fluid velocity in m/s, if the flow rate of a liquid through a circular pipe of 15
cm radius is 25 L/min.
(b)
What would the flow rate be (in kL/hr) from a 50 cm pipe with a fluid velocity of 0.5 m/s?
What is the importance of the Reynolds Number, apart from providing a relationship between the four
flow variables? The value of Re identifies the type of flow occurring in the bulk liquid. There are
three types of fluid flow, as shown in Figure 3.1.
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3. Fluid Flow
Laminar (Re < 2000)
Transitional (Re 2000-4000)
Turbulent (Re > 4000)
FIGURE 3.1 Different flow types and Reynolds Number values
Laminar flow is characterised by layering of liquids which flow almost independently of each other
without mixing, while turbulent flow has eddies and currents, resulting in more random movement,
and greater mixing across the cross section of the pipe. Transitional flow is a mixture of both, and the
fluid can change from laminar to turbulent and back again.
Think about a water tap as you turn it on more and more. The water begins flows in a steady
stream (laminar) but at its fastest flow, starts to break up, and even loses transparency as turbulence in
the stream creates bubbles.
CLASS EXERCISE 3.2
(a) For a given fluid (of fixed density and viscosity), what extremes of flow rate and pipe
size give rise to (i) laminar and (ii) turbulent flow?
Variable
Flow rate
Pipe diameter
(b)
Laminar
HIGH/LOW
Turbulent
HIGH/LOW
SMALL/LARGE
SMALL/LARGE
How could the Reynolds Number for a given fluid/pump/pipe combination be changed?
Why do engineers care how the fluid in a pipe moves as long as it comes out the other end?
It comes down to the mixing or lack of it occurring in the different flows. In laminar flow, the lack of
mixing means that heat transfer (as in a heat exchanger) will be poor, since convection will be limited,
while the opposite applies in turbulent flow. However, in turbulent flow, the build up of friction is
greater, and this results in pressure drops across the length of pipe, limiting the flow rates possible and
leading to less consistent flow.
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3. Fluid Flow
Pressure drops in pipes
To move fluids from one point to another, energy has to be expended by means of a pump, unless the
fluid will flow under gravity. Even in this case, a pump may be required to increase the flow rate,
where the downwards angle is not sufficient.
A pump provides the pressure necessary to move the fluid from one point to another. The
pressure from the pump must be greater than the pressure acting on the fluid from the other end of the
“pipe” for the movement to occur.
CLASS EXERCISE 3.3
What factors affect the pressure against which the pump must work?
Engineers tend to talk in terms of head, rather than pressure, but for the non-specialist, they mean
similar things. The total developed head (TDH) is the total resistance against which the pump is
working. This resistance is comprised of three general factors:
•
dynamic head – the flow resistance created by friction in piping, valves, fittings and liquid
viscosity
•
static head – the height required to which liquid must be raised
•
velocity head – the pressure required to accelerate the liquid to its flow velocity
If the location of the pipes is fixed, then nothing can be done about the static head. A certain flow rate
may be necessary for supplying a chemical reactor (or similar) and thus is also a fixed quantity.
Therefore, the dynamic head is the main variable which can be reduced so that the size of the pump is
as small (and therefore as cheap) as possible. The factors that affect dynamic head are:
•
the type of material from which the pipe is made
•
the flow rate
•
pipe diameter (and changes to the diameter)
•
the length of pipe
•
bends, junctions
•
the presence of valves (and how open they are)
The Fanning friction equation (Eqn 3.3) is used to estimate the dynamic (or friction) head, and while it
is not necessary for you to be totally proficient in its use, it does illustrate the key points of this topic.
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3. Fluid Flow
H=
fLv 2
5d
Eqn 3.3
where H is the dynamic head, f the Fanning friction factor (say that five times quickly!!), L the
equivalent length of straight pipe (in m), d the pipe diameter (in m) and the flow rate (in m/s).
The term “equivalent length of straight piping” is used to account for the presence of bends,
valves, junctions etc, and can be estimated from tables of correction factors for different fittings,
examples of which are shown in Table 3.1.
TABLE 3.1 Correction factors for fittings in equivalent length of straight pipes as the ratio L/d
Fitting
L/d factor
45° bend
16
90° bend
30
gate valve (open)
7
gate valve (½ open)
160
diaphragm valve (open)
105
diaphragm valve (½ open)
200
EXAMPLE 3.1
What is the effective length of straight pipe (diameter 50 mm), if two 10 m length lengths of
straight pipe are connected by a 45° bend?
The correction factor for a 45° bend is 16. The equivalent length is the factor multiplied by
the pipe diameter (0.05) which is 0.8 m.
This is added to the lengths of “real” straight pipe (10 + 10) to give an equivalent length of
20.8 m.
CLASS EXERCISE 3.4
Calculate the equivalent length of straight piping for the system described below with the
gate valve open and half open. The pipe diameter is 0.1 m.
5m
1m
0.5 m
7.5 m
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3. Fluid Flow
The value of the Fanning friction factor is dependent on the Reynolds number (16/Re for laminar
flow) and where turbulent flow is occurring, factors associated with the roughness of the pipe surface
come into play. We will not go into this any further here.
3.3 Pumps
Many different types of pumps have been designed to move fluids through pipe systems. There are
two common mechanisms by which a majority (but not all) of pumps work:
•
positive displacement pump – has an expanding cavity on the suction side and a decreasing
cavity on the discharge side; liquid flows into the pump as the cavity on the suction side
expands and the liquid flows out of the discharge as the cavity collapses
•
centrifugal pump – converts the input power to kinetic energy in the liquid by accelerating the
liquid by a revolving device, known as an impeller
CLASS EXERCISE 3.5
Use the Powerpoint slideshow provided to explain (in your words) how the following pumps
work, and to identify which are positive displacement and which are centrifugal:
•
piston
•
diaphragm
•
impeller
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3. Fluid Flow
•
gear
•
double acting force
•
peristaltic
•
simplex
•
vane
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3. Fluid Flow
Centrifugal pumps are used in a wide range of applications, and the more common type of pump in the
chemical industry because:
•
they are of simple construction with few moving parts
•
they have a long service life
•
maintenance is simple
•
they are relatively small and quiet
•
they can be installed in almost any position
•
they are vibration free
•
they are able to pump slurries and abrasive fluids
Their limitations are:
•
inability to pump high viscosity liquids
•
a difficult to accurately measure flow rate
Pumps for gases require different design elements because of the low density of liquids, and their
ability to be compressed. We will not cover gas pumps in this subject.
3.4 Valves
Valves are the controlling mechanism in fluid systems. They can control the flow rate by increasing
or decreasing the resistance to flow when opened or closed, as we have already seen. Valves can be
used for a number of different purposes:
•
on/off – only work fully open or fully closed
•
flow control – can be partly open
•
one-way – fluid cannot flow back through
•
pressure release
The valve mechanism can operate by:
•
closing down
•
sliding
•
rotating
CLASS EXERCISE 3.6
Draw diagrams that show how these different mechanism would control the flow.
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3. Fluid Flow
Valves generally work by having a moving disc or plug that is forced mechanically against a seat in
the valve body. When the disc is firmly against the seat, the valve is closed and fluid is prevented
from passing through, as can be seen in Figure 3.2.
(a)
(b)
(c)
FIGURE 3.2 Valve (a) fully open (b) partly open (c) closed
Some of the common valve types are:
•
diaphragm (Figure 3.2)
•
globe (Figure 3.3(a))
•
ball (Figure 3.3(b))
•
gate (Figure 3.3(c))
•
needle
•
butterfly
•
plug
•
check (see piston & diaphragm pump diagrams)
(a)
(b)
FIGURE 3.3 (a) Globe (b) ball valve
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3. Fluid Flow
(c)
FIGURE 3.3 (c) Gate valve
What You Need To Be Able To Do
•
define important terminology
•
perform fluid dynamics calculations
•
explain the significance of fluid dynamics
•
name and explain how different pump types work
•
name and explain how different valve types work
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