FLOW AND TRANSPORTATION OF FLUID AND HEAT
Syllabus:
1.
Flow of fluids: Fluid statics, Manometers, Reynolds
number, Bernoulli’s theorem, fluid heads, Friction losses, Measurement of fluid
flow meters -
Orifice meter, Venturimeter, Pitot tube, Rotameter and Displacemeter.
2.
Transportation of fluids, pipe, joints, valves,
reciprocating piston, duplex, diaphragm, rotary, centrifugal and turbine pumps.
Questions:
Flow of fluids:
1.
Bernoulli’s theorem. (91, 95) [8]
2.
State and explain the significance of Bernoulli’s
equation and Reynolds number with regards to flow of fluids. (92, 96) [8 + 8]
3.
Fluid head and friction losses - short notes. (93, 94,
95) [8]
4.
Derive Bernoulli’s equation to prove the conservation
of energy during the flow of fluids. (94) [8]
Measurement of fluid
flow meters:
Short notes on
1.
Displacemeter (91) [8]
2.
Pitot tube (92, 93, 95) [4]
3.
Venturimeter (93, 95) [8]
4.
Fluid flow meters / displacemeters. (94) [8]
5.
Manometer (93) [8]
6.
Measurement of fluid flow by Orifice meter,
Venturimeter and Rotameter.
Transportation of
fluids
1.
Rotary centrifugal and Turbine pumps. (91, 93) [8]
2.
Turbine pumps (92) [4]
3.
Pumps (94) [8]
4.
Centrifugal (volute) pump (94`) [4]
5.
Diaphragm pump (94`) [4]
6.
Rotary (gear) pump (94`) [4]
7.
Reciprocating piston and Duplex pump (95) [16]
8.
Describe briefly the different pumps and for
transportation of fluids (93, 96) [16]
INTRODUCTION
Fluid includes both liquids and gases.
·
Fluids may be defined as a substance that does
not permanently resist distortion. an attempt to change the shape of a mass of
fluid will result in layers of fluids sliding over one another until a new
shape is attained.
During
the change of shape shear stresses
will exist, the magnitude of which depends upon the viscosity of the fluid and
the rate of sliding. But when a final shape is reached, all shear stresses will
disappear. A fluid at equilibrium is free from shear stresses.
·
The density of a fluid changes with temperature
and pressure. In case of a liquid the density is not appreciably affected by
moderate change of pressure.
In
case of gases, density is affected appreciably by both change of temperature
and pressure.
·
The science of fluid mechanics includes two
branches:
(i) fluid statics and (ii) fluid dynamics.
Fluid statics
deals with fluids at rest in equilibrium.
Fluid dynamics
deals with fluids under conditions where a portion is in motion relative to
other portions.
FLUID STATICS
Hydrostatic pressure
In a
stationary column of static fluid the pressure at any one point is the same in
all directions. The pressure will also remain constant in any cross-section
parallel to the earth’s surface, but will vary from height to height.
Let us consider, that the column of fluid in the figure is
remaining at equilibrium. If the orifice D is open then the fluid will try to
flow away. So either D is closed or a pressure is applied such that the liquid
column stand at any desired height. The cross-section of the column is S (let).
Now, say the pressure at the height X2 = P2 (in
gravitational unit). At equilibrium all the forces acting on point B will be
the same.
i.e. Upward force
=P2S
 |
Downward forces:
Force
given by atmosphere = P1S
Force
given by fluid column of height h1 = (h1r g/gc)S
Where, r is the density of the fluid.
At equilibrium upward and downward forces are equal at point
B.
\
P2S = P1S +
h1 r
S g/g c eqn.
(1)
where, each term of force is expressed in gravitational
units i.e. lbf, gm-wt, kg-wt etc.
g/gc » 1.0 so equation (1) can be written as
P2S
= P1S + h1 r S
P2
= P1 + h1 r eqn.
(2)
Similarly, P3 =
P2 + (h2 - h1) r
=
P1 + h1 r + h2 r - h1 r
=
P1 + h2 r
=
P1 + (X1 - X3) r [since h2 = X1 - X3 ]
We can thus generalize for any point in the fluid, the
pressure will be
Pn = P1 + r DX where DX = X1 - Xm.
or, Pn
-
P1 = r DX
or, DPn = r DX eqn.
(3)
i.e. the
pressure difference (DPn) between any two points can be measured by
the vertical distance between those two points, multiplied by the density of
the fluid.
Since in
equation (3) there is no term involving the cross-sectional area (S), it is not
necessary that the vertical column be of uniform cross-section.
i.e. the
shape may be any of the following types:
MANOMETERS
Simple Manometer
Manometers are used to measure the pressure of any fluid.
A U-tube is filled with a
liquid A of density rA.
The arms of the U-tube above liquid A are filled with fluid B which is immiscible
with liquid A and has a density of rB. A pressure of P1 is exerted in one arm of
the U-tube, and a pressure P2 on the other. As a result of the difference in
pressure (P1 - P2) the
meniscus in one branch of the U-tube will be higher than the other branch.
The vertical distance between these two surfaces is R. It is the purpose of the manometer to
measure the difference in pressure (P1 - P2) by means of the reading R.
At equilibrium the forces at the two points (2 and 3) on
the datum plane will be equal.
Let the cross sectional area of the U-tube be S.
** All the forces are
expressed in gravitational unit.
Total downward force at
point (2) = Forces at point (1)
+ force due to column of fluid B in between
points (1) and (2).
= P1S + (m + R) rB
(g / gc) S
Total downward force at
point (3) = Force at point (5)
+ Force
due to column of fluid B in between points (5) and
(4)
+ Force due to column of liquid A in between
points (4) and (3)
= P
2S + m r
B (g/gc) S + R rA (g/gc) S
At equilibrium:
Force at point (2) = Force
at point (3)
or, P1S
+ (m + R) rB
(g / gc) S = P 2S + m r
B (g/gc) S + R rA (g/gc) S
or, P1
-
P2 = R rA (g/gc)
+ m rB
(g/gc) -
m rB
(g/gc) -
R rB
(g/gc)
= R (rA - rB)
g/gc.
 |
or, D P = P1 - P2 = R (rA - rB)
g/gc.
It should
be noted that this relationship is independent of the distance ‘m’ and cross
sectional area ‘S’ of the U-tube, provided that P1 and P2
are measured from the same horizontal plane.
DIFFERENTIAL MANOMETER
Fig. Differential manometer
For the
measurement of smaller pressure differences, differential manometer is used.
The
manometer contains two liquids A and C which must be immiscible.
Enlarged
chambers are inserted in the manometer so that the position of the meniscus 2
and 6 do not change appreciably with the changes in reading.
So the distance between (1) and (2) = Distance
between (6) and (7)
Total downward force on point (3)
Fleft = P1S + a rA
g/gc S + b rA g/gc S
Total downward force on point (4)
Fright = P2S + a rB
g/gc S + d rA g/gc S + RrC
g/gc S
At equilibrium
Fleft
= Fright.
\ P1S + a rA
g/gc S + b rA g/gc S = P2S + a rB
g/gc S + d rA g/gc S + RrC
g/gc S
P1 - P2 =
(d -
b) rA
g/gc + RrC
g/gc
= - R rA
g/gc + RrC
g/gc.
= R (rC
- rA ) g/gc
D P =
P1 -
P2 = R (rC
- rA ) g/gc
From this it follows that the smaller the
differences rC
- rA ,the larger
will be the reading R on the manometer for a given value of DP.
INCLINED MANOMETER
Fig. Inclined
manometer
For measuring small difference in pressure
this type of manometer is used.
In this type of manometer the leg containing one meniscus
must move a considerable distance along the tube. Here the actual reading R is
magnified many folds by R1, where
R = R1
sin a
where a is the angle of
inclination of the inclined leg with the horizontal plane.
In this case DP = P1 - P2
= R (rA - rB
) g/gc.
In this type of gauge it is necessary to provide an
enlargement in the vertical leg so that the movement of the meniscus in this
enlargement is negligible within the range of the gauge.
By making a small the value of R is multiplied into a much larger
distance R1.
FLUID DYNAMICS
Reynolds’ Experiment
This experiment was performed by Osborne Reynolds in
1883. I Reynolds experiment a glass tube
was connected to a reservoir of water in such a way that the velocity of
water flowing through the tube could be varied.
At the inlet end of the tube a nozzle was fitted through
which a fine stream of coloured water can be introduced.
After
experimentation Reynolds found that when the velocity of the water was low the
thread of color maintained itself through the tube. By putting one of these
jets at different points in cross section, it can be shown that in no part of
the tube there was mixing, and the fluid flowed in parallel straight lines.
As the velocity was increased, it was found that at a definite
velocity the thread disappeared and the entire mass of liquid was uniformly
colored. In other words the individual particles of liquid, instead of flowing
in an orderly manner parallel to the long axes of the tube, were now flowing in
an erratic manner so that there was complete mixing.
When the fluid flowed in parallel straight lines the
fluid motion is known as Streamline flow
or Viscous flow.
When the fluid motion is erratic it is called turbulent
flow. The velocity at which the flow changes from streamline or viscous flow to
turbulent flow it is known as the critical
velocity.
THE REYNOLDS NUMBER
From Reynolds’ experiment it was found that critical
velocity depends on
1.
The internal diameter of the tube (D)
2.
The average velocity of the fluid (u)
3.
The density of the fluid (r) and
4.
The viscosity of the fluid (m)
Further, Reynolds showed that these four factors must be
combined in one and only one way namely (Dur / m) . This function (Dur / m) is
known as the Reynolds number. It is a dimensionless group.
it has been shown that for straight circular pipe, when
the value of the Reynolds number is less than 2000 the flow will always be
viscous.
i.e. NRe
< 2000 Þ viscous
flow or streamline flow
NRe > 4000 Þ turbulent flow
Dimensional analysis of Reynolds number
[D] = L (ft)
[u] = L/q (ft / sec)
[r] = M / L3 (lb/ft3)
[m] = M / (Lq) {lb/(ft sec)}
= 1 Þ
dimensionless group
 |
BERNOULLI’S THEOREM
When the
principle of conservation of energy is applied to the flow of fluids, the
resulting equation is called Bernoullis
theorem.
Let us
consider the system represented in the figure, and assume that the temperature is uniform through out the system. This
figure represents a channel conveying a liquid from point A to point B The pump
supplies the necessary energy to cause the flow. Let us consider a liquid mass m (lb) is entering at point A.
Let the pressure at A and b are PA and PB
(lb-force/ft2) respectively.
The average velocity of the liquid at A and B are uA
and uB (ft/sec).
The specific volume of the liquid at A and B are VA
and VB (ft3/lb).
The height of point A and B from an arbitrary datum plane
(MN) are XA and XB (ft) respectively.
Potential energy at point A, (W1)= mgXA
ft-poundal [absolute unit]
=
m (g/gC)XA ft-lb force = mXA ft-lb force [gravitational unit]
Since the liquid is in motion
\
Kinetic energy at point A, (W2) = 1/2.
m uA2 ft-poundal
=
(1/2. m uA2 )/ gC pound-force
As the liquid m enters the pipe it enters against pressure of
PA lb-force/ft2 and therefore.
Work against the pressure at point A, (W3) = mPAVA ft-lbf.
N.B. Force at point A = PA S [S =
Cross-section area]
Work done against force PA
S = PA (S h) = PA V
\
Total energy of liquid m entering
the section at point a will be (E1) = W1 + W2 + W3
E1 = [ mXA
+ (1/2. m uA2 )/ gC + mPAVA ]
ft-lbf.
After the system has reached the steady state when ever m (lb) of liquid enters at A another m
(lb) pound of liquid is displaced at B according to the principle of the
conservation of mass. This m (lb)
leaving at B will have ab energy content of
E2 = [ mXB
+ (1/2. m uB2 )/ gC + mPBVB ]
ft-lbf.
Energy is added by the pump. Let the pump is giving w ft-lbf / lb energy to the
liquid
E3 = m w ft-lbf.
Some energy will be converted into heat by friction. It has
been assumed that the system is at a constant temperature, hence, it must be
assumed that the heat is lost by radiation or by other means. Let this loss due
to friction be F ft-lbf / lb of liquid.
E4 = - mF ft-lbf [negative sign for loss]
\
The complete equation representing an energy balance across the system between
points A and will therefore be
E1 + E3 +
E4 = E2
or, mXA + (1/2. m
uA2 )/ gC
+ mPAVA + m w
-
mF =
mXB + (1/2. m uB2
)/ gC + mPBVB
Now, the unit of energy term is ft-lbf / lb
\
The BERNOULLI’S THEOREM.
The density of the liquid r be expressed lbm
/ ft3, then
VA
= 1 / rA
and VB = 1 / rB
then Bernoulli’s equation can be written in the form also
FLUID HEADS
All the
terms in Bernoulli’s theorem have unit of ft-lbf
/ lbm which is
numerically equal to ‘ft’ only. That
is each and every time terms can be expressed by height.
Dimensional Analysis
[ft] = L
[lbf] = (MLq -2)
/ (Lq-2) = M
[lbm] = M
[ft-lbf / lbm ] = LM / M = L
That is
every term has a dimension of length (or height) if the terms are expressed in
gravitational unit. This height are termed as heads in the discussions of hydraulics. Each term has different
names:
Potential
heads XA
, XB.
Velocity
heads UA2
/ (2 gC ), UB2 / (2 gC )
Pressure
heads PA
VA , P A rA , PB VB , PB
rB
.
Friction
head F
Head added by the pump w
FRICTION LOSSES
 |
In
Bernoulli’s equation a term was included to represent the loss of energy due to
friction in the system. The frictional loss of a fluid flowing through a pipe
is a special case of general law of the resistance between a solid and fluid in
relative motion.
Let us
consider a solid body of any designed shape, immersed in a stream of fluid.
Let, the area of contact between the solid and f fluid = A
If the
velocity of the fluid passing the body is small in comparison to the velocity
of sound , it has been found experimentally that the resisting force depends
only on the roughness, size and shape of the solid and on the velocity ,
density and viscosity of the fluid. Through a consideration of the dimensions
of these quantities it can be shown that,
where, F = total
resisting force
A = area of
solid surface in contact with fluid
u =
velocity of the fluid passing the body
r =
density of fluid
m =
viscosity of fluid
gc
= 32.2 (lbm ft )/ (lbf
s2)
f
= some friction whose precise form must
be determined for each specific case.
The form of function f depends upon the
geometric shape of the solid and its roughness.
 |
FRICTION IN PIPES
In a
particular case of a fluid flowing
through a circular pipe of length L, the total force resisting the flow must
equal the product of the area of contact between the fluid and the pipe wall
and F/A of the friction loss equation.
The pressure drop will be:
where DPf = pressure drop due to friction (lb/ft2)
F / A = resisting force (ft-lbf per ft2
of contact area)
L = length of pipe (ft)
D = inside diameter of the pipe (ft)
r = density of fluid (lbm /
ft3)
u = average velocity of fluid (ft / s)
m = viscosity of fluid (lbm /
ft / s)
gc = 32.2 (lbm ft / lbf
s2)
For many decades Fanning’s equation was used:
 |
In Fanning’s equation the value of ‘f ’ was taken from tables. This equation however has been widely
used for so many years that most engineers still use the Fanning’s equation,
except that instead of taking values of ‘f’ from arbitrary tables a plot
of the equation f = (Dur / m) is used.
The graph (graph 1)
is not that much accurate : Error: ± 5 to 10 % may be expected for laminar flow
By combining Hagen Poiseulles equation a new simple form of
equation can be obtained.
MEASUREMENT OF FLUID FLOW
Methods of measuring
fluids may be classified as follows:-
1) Hydrodynamic methods 2)
Direct displacement 3) Dilution method and
(a) Orifice meter (a)
Disc meters 4) Direct weighing or measuring
(b) Venturimeter (b)
Current meters
(c) Pitot tube
(d) Rotameter
(e) Weirs
ORIFICE METER
 |
Objective:
To measure the flow of
fluids.
i) Velocity of fluid through a pipe (ft/sec)
ii) Volume of liquid passing per unit time (ft3/sec,
ft3/min, ft3/hr).
Description
An orifice meter is considered to be a thin plate
containing an aperture through which a fluid issues. The plate may be placed at
the side or bottom of a container or may be inserted into a pipe line.
A manometer is fitted outside the pipe. One end at point
A and the other end at point B (see fig.). The pressure difference between A
and B (i.e. before and after the orifice) is read, and the reading is then
converted to fluid flow-rate.
Derivation
Bernoulli’s equation is written between these two points,
the following relationship holds
|
Conditions
|
Equation (1) changes to:
|
|
i) The pipe is
horizontal
\ XA
= XB.
|
 |
|
ii) If frictional
losses are assumed to be inappreciable then F = 0
|
 |
|
iii) If the fluid is a
liquid then
rA » rB = r (let)
|
 |
|
iv) Since no work is
done on the liquid, or by the liquid between A and B.
\ w = 0
|
 ............................ (2) |
Equation (2) may be
written as:
........................(3)
Since, PA – PB = DP,
and since 
= DH
= DH
\ equation (3) can be
written as
.........................................(4)|
N.B. PA = HA
r g / gc
PB
= HB r g / gc
PA – PB = (HA – HB )r g / gc
or, DP = DH r g / gc.
Since, g / gc » 1.0 hence, DH = DP / r
If the pipe to the right of the orifice plate were removed so that
the liquid issued as a jet from the orifice, the minimum diameter of the
stream would be less than the diameter of the orifice. This point of minimum
cross-section is known a vena-contracta.
|
Point B was chosen at the vena-contracta. In practice the
diameter of the stream at the vena-contracta is not known, but the orifice diameter
is known. Hence equation (4) may be written in terms of the velocity through
the orifice, as a result a constant (Co) has to be inserted in the equation (4)
to correct the difference between this velocity and the velocity at the
vena-contracta. There may be some loss
by friction and this also may be included in the constant. Equation (4) then
becomes:
............................(5)
where U0 =
velocity through the orifice.
The pressure difference DP
between A and B is read directly from the manometer.
In equation (5)
DH is measured from manometer (DP/r)
gc is constant
C0 is constant and known for a particular
orifice meter.
U0 and UA is unknown
So to solve both U0
and UA another equation is required. We can assume that the volume
flow-rate at A and orifice are equal, we can thus deduce the following
equation.
or, 
..................................(6)
where, dP = diameter of pipe
dO = diameter of orifice
dP and dO are already known
Now we can solve equation
(5) and (6) to get the value of both UA and UO.
UA = velocity
of fluid in the pipe
= volume flow rate of
fluid in the pipe.
The constant Co depends
on the
·
ratio of the orifice diameter to the pipe
diameter
·
position of the orifice taps
·
value of Reynolds number for the fluid flowing
in the pipe.
*** For values of
Reynolds number (based on orifice diameter i.e. 
of 30,000 or above,
the value of Co may be taken as 0.61.
of 30,000 or above,
the value of Co may be taken as 0.61.
Advantage
It is very simple device and can be easily installed i.e.
cost of installation is less.
Fluids of various viscosity can be measured just by
changing the orifice diameter.
Disadvantage
The orifice
always results in a permanent loss of pressure (head), which decreases as the
ratio of orifice diameter to pipe, diameter increases i.e. cost of operation,
particularly for long term, is considerable.
 |
VENTURIMETER
Description
The
venturimeter, as shown in the figure consists of two tapered sections inserted
in the pipeline, with the tapers smooth and gradual enough so that there are no
serious loss of energy. At point B the section of venturimeter has minimum
diameter. This point is called the ‘throat’ of the venturimeter.
The
venturimeter is fitted within a pipe. The pressure difference at A and B is
measured by a manometer.
Derivation
If the
Bernoulli’s equation is written between these two points the following
relationship holds.
|
Conditions
|
Equation (1) changes to:
|
|
i) The pipe is
horizontal
\ XA
= XB.
|
|
|
ii) If frictional
losses are assumed to be inappreciable then F = 0
|
|
|
iii) If the fluid is a
liquid then
rA » rB = r (let)
|
|
|
iv) Since no work is done
on the liquid, or by the liquid between A and B. i.e. w = 0
|
............................ (2) |
Equation (2) may be
written as:
........................(3)
Since, PA – PB = DP,
and since = DH
= DH
\ equation (3) can be
written as
.........................................(4)|
N.B. PA = HA
r g / gc
PB
= HB r g / gc
PA – PB = (HA – HB )r g / gc
or, DP = DH r g / gc.
Since, g / gc » 1.0 hence, DH = DP / r
If the pipe to the right of the orifice plate were removed so that
the liquid issued as a jet from the orifice, the minimum diameter of the
stream would be less than the diameter of the orifice. This point of minimum
cross-section is known a vena-contracta.
|
Since there are practically no losses dude to eddies and
since the cross-section of the high velocity part of the system is accurately
defined hence equation (4) may be written as
............................(5)
where UB =
velocity at the throat of the venturimeter
In case of venturimeter the value of coefficient CV = 0.98.
Comparison between
orificemeter and venturimeter:
|
Orifice meter
|
Venturimeter
|
|
1.
Installation is cheap and easy.
2.
The power loss is considerable in long run.
3.
They are best used for testing purposes or other
cases where the power loss is not a factor, as in steam lines.
4.
Installing a new orifice plate with a different
opening is a simple matter.
|
1.
Installation is costly. It is less easier than
orifice meter. (Disadvantage)
2.
Power loss is less in long run even negligible (Advantage)
3.
Venturimeters are used for permanent installation.
4.
Installation of a different opening require
replacement of the whole venturimeter. (Disadvantage)
|
PITOT TUBE
The pitot
tube is a device to measure the local velocity along a streamline. The
configurations of the device are shown in the figure. The manometer has two
arms. One arm ‘a’ is placed at the center of the pipe and opposite to the
direction of flow of fluid. The second arm ‘b’ is connected with the wall of
the pipe. The difference of liquid in two arms of the manometer is the reading.
The tube in
the ‘a’ hand measures the pressure head (XA) and the velocity head 
. The ‘b’ hand measures only pressure head (XB).
. The ‘b’ hand measures only pressure head (XB).
or, 
or, 
.........(i)
Here DXB
is the pressure head of the fluid whose flow is to be measured that corresponds
to R.
Since the manometer measures the pressure according to the
following equation.
or, 
[Since
g/gC »
1]
[Since
g/gC »
1]
where, r‘ = density of the liquid in the manometer
r =
density of the fluid in the pipe.
Replacing DX in the equation (i) gives,
[U
= UA (let)]
\ 
...................................(ii)
...................................(ii)
The velocity measured is the
maximum velocity inside the pipe.
By orifice meter or venturimeter average velocity of fluid
is measured. With pitot tube velocity of only one point (i.e. at the center of
the pipe) is measured. To convert Umax to average velocity 
the following relationship is taken into concern.
the following relationship is taken into concern.
where, D = diameter of
the pipe
Umax
= maximum velocity of fluid
r =
density of the fluid flowing
m =
viscosity of the fluid flowing
average velocity in the pipe
Disadvantage of pitot
tube
1.
It does not give the average velocity directly.
2.
When velocity of gases are measured the reading are
extremely small. In these cases some form of multiplying gauge like
differential manometer and inclined manometers are used.
 |
where D= diameter of the
pipe
Umax = maximum
velocity of fluid
r = density of the fluid
flowing
m = viscosity of the fluid
flowing
U = average velocity in
the pipe
ROTAMETER
ROTAMETER
 |
Construction of
rotameter:
It consists
essentially of a gradually tapered glass tube mounted vertically in a frame
with the large end up. The fluids flow upward through the tapered tube.
Inside the
tapered tube a solid plummet or float having diameter smaller than that of the
glass tube is placed. The plummet rises or falls depending on the velocity of
the fluid.
Principles of
rotameter:
For a given
flow rate, the equilibrium portion of the float in the rotameter is established
by a balance of three forces.
1.
The weight of the float (w)
2.
The buoyant force of the liquid on the float (B)
3.
The drag force on the float (D)
‘w’ acts
downward and B and D acts upward.
At equilibrium:
W =
B + D
or, D =
W – B
or, FD gC
= Vf rf
g –
Vf r g .
where, FD =
drag force
Vf
= volume of float
rf
= density of float
r =
density of fluid
The quantity of Vf can be replaced by 
, where mf is the mass of the float, and equation
(i) becomes: FD gC =
Vf (rf – r) g = 
= 
, where mf is the mass of the float, and equation
(i) becomes: FD gC =
Vf (rf – r) g = =
For a given
meter operating on a certain fluid, the right-hand side of equation- (ii) is
constant and independent of the flow rate. Therefore FD is also
constant, when the flow increases the
position of the float must change to keep the drag force constant.
where, K1
= constant
If the tube
is tapered, and difference between the diameters of float and tube are small
then it can be shown that the height at which the plummet is floating is
proportional to the rate of flow.
Advantages:
1.
The flow rates can be measured directly.
2.
Measured in linear scale and
3.
Constant and small head loss.
DISPLACEMENT METERS
Displacement meters covers devices for measuring liquids
based on the displacement of a moving
member by a stream of liquid. These meters may be classified as disc meters and current meters.
DISCMETER
The figures
share a typical discmeter. The displacement member in this apparatus is a
hard-rubber disc. This disc is mounted in a measuring chamber which has a
conical top and bottom. The disc is so mounted that it is always tangent to the
top cone at one point and to the bottom cone at a point 1800
distant.
 |
The measuring chamber has a partition that extends half way
across it, and the disc has a slot to take this partition.
The
measuring chamber is set into the meter body in such a way that the liquids
enters at one side of the partition, passes around through the measuring
chamber, and out on the other side of the partition.
Whether the
liquid enters above or below the disc, it moves the disc in order to pass, and
this and this motion of the disc results
in the axis moving as though, it were rotating around the surface of a cone
whose apex is the center of the disc and whose axis is vertical. This motion of
the axis of the disc is translated through a train of gears to the counting
dial (not shown in the figure).
CURRENT METER
The
displacement member is a turbine wheel which is delicately mounted so that it
moves with the minimum of friction. The stream of water entering the meter
strikes the buckets on the periphery of the wheel and makes it rotate at a
speed proportional to the velocity of the water passing through the meter.
N.B. Both discmeter and current meter measures the total
volume of liquid that has passed.
PUMPS
Reciprocating pumps: Piston, Duplex, Diaphragm
Rotary pumps: Centrifugal, Volute, Turbine, Gear
Pump is the device that
moves the fluid through a pipe.
Minimum configuration of a pump: Cylinder,
piston or
plunger,
power to
drive the piston and
valves.
RECIPROCATING PUMPS
1. PISTON TYPE
A1, A2 : Piston, B: Piston packing, C:
Cylinder liner, E1, E2: Suction valves, F1,F2:
Discharge valves, H: Valve decks, M: Piston rod.
Construction
The pump in the figure has single water cylinder – hence
called simplex pump. The pump consists:
(i)
A piston consisting essentially of two discs A1
and A2 with rings of packing B between them. The piston operates
within a removable bornze liner, C.
(ii)
The lower row of valves, E1 and E2
are suction valves, in the upper row F1 and F2 are
discharge valves.
(iii) The
overall assembly is packed within an air-tight casing.
Operation
(i)
If the piston is moving from left to right, it will
create a suction on the left hand side which will open the left hand suction
valves E1 and close the left hand discharge valves F1.
(ii)
At the same time a pressure is develop on the right
hand side which will close the E2 suction valves and open F2
discharge valves.
This pump is double acting , because it displaces
water on both halves of the cycle.
The pump
requires minimum 4 valves.
Uses
·
This type of pump is suitable for pressure heads
upto 150 to 200 ft and for any liquids that are not viscous, corrosive or
abrasive.
·
The valve type is deck valves, hence it cannot
withstand very high pressure.
RECIPROCATING DUPLEX PUMP
Duplex plunger pump–longitudinal
section
A1, A2: Water plungers, B1,B2:
Piston rod, C1, C2: Suction valves, D1, D2:
Discharge valves, E: Packing ring, F: Partition.
Construction
The pump in
the figure consists of two water cylinders, hence called duplex pump.
The pump consists:
(i)
Two plungers are packed inside the cylinders. Two
stationary packing ring in between the plungers and the cylinders.
(ii)
Two suction valves, C1,C2
and two discharge valves D1, D2 are provided.
(iii) the
cylinder is divided into two parts by a partition F.
Operation
(i)
Both the plungers act synchronously. When left plunger
A1, is producing suction, right plunger A2 increases the
pressure.
(ii)
When plunger A1 produce suction pressure,
suction valve C1 opens and discharge valve D1 remains
closed. At the same time plunger A2 produce pressure so discharge
valve D2 opens while suction valve C2 remains closed.
Use
(i)
When pump liquids contains suspended matter that may
abrade the packing so that replacement are more frequent then this type of pump
is useful.
(ii)
Since the valves are of pot-valve type hence can be
used under high pressure.
RECIPROCATING DIAPHRAGM
PUMP
Construction
In the
figure of diaphragm pump instead of a piston or plunger it employs a flexible
diaphragm with a discharge valve attached to the shaft the discharge valve is
flap type]. it also has a suction valve.
Operation
When the
shaft is moved upward the chamber C experiences partial vacuum and suction
valve is opened and liquid comes in. When the shaft goes down the discharge
valve opens and suction valve closes – the liquid comes out of the pump.
Uses / Advantages
(i)
Since it has no
moving parts except the flexible diaphragm and the valve, since its
construction is rugged and simple and repairs are easily made, it is suited for
the most severe services.
(ii)
It is the most satisfactory pump available for handling
liquids with large amounts of solids in suspension under low pressure.
(iii) By
adjusting the diaphragm the stroke may be varied and the discharge controlled within accurate limits.
 |
ROTARY PUMP
(i)
Rotary positive displacement pump
(ii)
Centrifugal pump
ROTARY POSITIVE DISPLACEMENT PUMP
Construction
The pump
consists of essential two gears, which match with each other and which run in
close contact with the casing. The number of teeth of the gears varies from two
or more in each wheel.
Operation
Slugs of liquids are cut between the gear teeth and the
casing, carried around next to the casing and forced out through the discharge
pipe.
Use
(i)
Such a pump handles viscous or heavy liquids.
(ii)
Since the performance of positive displacement rotary
pump depends on maintaining a running fit between the rotating member and the
casing it is not desirable to use this pumps on liquids that carry solids in
suspension.
(iii) They
are used to handle quite stiff pastes, semifluid waxes and similar material can
be handled with those pumps when the speed is not too high.
CENTRIFUGAL PUMP
The main
principle of these pumps is that the liquid is sucked from the centre of an
impeller and thrown centrifugally upwards to the periphery from where liquid is
discharged.
Centrifugal
pumps are of two distinct types, Volute
type and Turbine type.
Construction
The
simplest form of the centrifugal pump is the single-stage single suction, open
runner volute. The most important member of the centrifugal pump is the impeller
or runner. This consist essentially of a series of curved vanes
extending from a hub. This is maintained in the casing of the
pumps in such a way that the two halves of the casing are as near by as
possible in contact with the surface of these vanes.
Operations
Water
entering at the suction connection is thrown outward by the rotation of the
vanes. As the liquid leaves the vanes and enters the volute of the casing , the
velocity is increased according to Bernoulli’s theorem therefore, its
pressure must be correspondingly increased and this increase in pressure is the
source of the head developed by the pump.
Disadvantages
In case of
open impeller system there are two main power losses:
(i)
The water which was thrown out radically by the vanes
must suddenly change its direction as it enters the volute. Any such sudden
change in direction involves turbulence which consumes power in the form of
friction.
(ii)
These are cheap pumps and therefore not accurately
finished. This fit between the impeller and the casing is usually poor and
therefore there is leakage from the discharge side back to the suction side.
To prevent this loss by leakage from the discharge side to
the suction side, the closed impeller system has bee developed. In this case
the vanes of the impeller are enclosed between two rings.
TURBINE CENTRIFUGAL PUMP
Construction
Turbine
pumps consists of an impeller with vanes, a diffusion ring
– they are fitted in a casing. The diffusion ring is stationary. The liquid is
discharged in a volute.
Operation
In case of
volute pumps the principal energy loss was due to turbulence that occurs at the
point where the liquid changes its path from radial flow (due to the action of
the impeller) to tangential flow in the discharge volute. The diffusion ring in
a turbine pump cause the liquid to make this change in direction smoothly and
without shocks or eddies. The liquid issuing from the tip of the impeller is
caught in these passages and turned gradually and smoothly into the discharge
volute.
Use
Turbine pumps is reserved for clear, non-viscous and
non-corrosive liquids.