Transcript Measurement lecture 3

MEASUREMENTS
AND
INSTRUMENTATION
LIQUID LEVEL AND QUANTITY
MEASUREMENT
 Level measurement may be required to give an accurate
value of level for various purposes such as
 In a supply of liquid at a constant head from a tank
 Accurate quantity in aircraft fuel tanks
 To be aware of a point when a tank is to be
replenished before it emptied.
2
Liquid level can be measured by
1)
i.
•
Direct methods:
Dipstick
For open tank an interval scale may be fitted, if
convenient.
Depth scale
3
ii.
Sight glass
• For a closed tank or boiler, an external sight glass may be
used. But if the fluid is at high pressure, glass guard and stop
cocks are necessary for personnel protection.
• It can be used up to 700 MPa and 300 °C.
stop cocks
Guard and scale
Sight glass
Metal
connections
4
2)
i.
•
Indirect Methods:
Floating ball
This is a simplest form where the float is attached to a cable
which is wound around a pulley to which the indicating pointer
is attached. The movement of the pointer as a level rise or
decrease indicate the level on a scale calibrated in terms of the
level of tank
Scale
Pulley
Float
Counter
balance
Types of floats used are:
• Hollow metal spheres
• Disc and
• Ceramic floats
h
5
ii.
Pressure method
Since the pressure P due to a column h of fluid of constant density ρ is
given by P=ρgh, then h=P/ρg. A measure of the pressure difference
between the surface and the bottom of the liquid will give a measure
of the level of that liquid in tank.

Opened tank
In a vented tank a simple u-tube mercury manometer is used.
Fig. Vented tank (u-tube fitted at bottom of the tank)
6
Pressure method Cont…
A level Z-Z
L.H.S Pressure = R.H.S Pressure
Pa + ρgh + ρgy = Pa + ρmghm
ρh = ρmhm – ρy
When the mercury levels were initially at the same height as the
base of the tank, Then:
hm
y
2
hm
h   m hm  
2
 m hm hm
h


2
7
Pressure method Cont…
 m 1 
h  
 hm
  2
• Also
h  khwhere
m

1
K   m  
  2
8
Pressure method Cont…
• Closed Tank
When the tank is pressurized or closed, the
simple u-tube will give false reading unless the
end of a tube is connected to the space above
the liquid.
9
Pressure method Cont…
10
Pressure method Cont…
At level Z-Z
LHS Pressure = RHS pressure
Pi + ρgh + ρgy1 + ρmghm = Pi + ρgh1 + ρgy2
ρh + ρy1 + ρmhm = ρh1 + ρy2
Since the mercury levels are both yo below the tank bottom when
h
h=h1, then
And
hm
y y  m
1
o
2
y 2  yo 
Substituting these values into above equation, we have
2
hm 
hm 


h    yo     m hm  h1    yo  
2
2


11
Pressure method Cont…
hm
hm
h  yo  
  m hm  h1  yo  
2
2
Rearranging and making h term the subject
hm
hm
h  h1       m hm
2
2
h  h1  hm  mhm
Divide by density of measured liquid throughout and
rearranging, we will have
 m 
h  h1  hm 
 1
 

Also
 m 
h  Khm , where k   
 1
 

12
iii.
Weight method

Load cells
•
In many applications, the measurement of level is a means
of measuring the total quantity of fluid, either the volume
or the mass.
•
In industrial applications, it is more convenient to measure
the force exerted by gravity on the tank and its contents.
This is conveniently done by mounting the tank on the load
cells(strain-gauge type or hydraulic type) which measure
the weight of the fluid contained in the tank
13
Weight method cont…
Force on the load cells is given
by:
A
 F  Mg  Ahg
Tank
Then mass content of the fluid
F

m  Ah 
Content
g
Volume content = Ah   F
g
and the head (h) of the fluid,
h  F
h
F
1
F
2
Load
cells
Ag
14
MEASUREMENT OF SPEED
•
Mean speed is either measured for linear or
rotational movements of an object or a point in
mechanism with respect to time i.e.
Vmean =
ωmean =
•
S linear

velocity
t
Q
angular velocity
t
However, the instantaneous linear or angular
velocity is of greater interest, and this may be
measured in several ways.
1.
2.
Mechanical Tachometer
Centrifugal – force tachometer
15
MEASUREMENT OF SPEED cont…
Mechanical tachometer
Fig. Centrifugal – force tachometer
As a shaft rotates, centrifugal force developed by the rotating
balls work to compress the spring as a function of speed and
accordingly position a pointer on a scale (velocity calibrated.
2
Mv
Centripetal force = Ma =
r
It can measure speed up to 40,000 R.P.M and are usually used to
make and break circuit for speed control (governor)
16
MEASUREMENT OF SPEED cont…
Electrical Tachometer
o An electrical tachometer consists of a transducer which
converts rotational speed into an electrical signal coupled to
an indicator.
o Eddy-current or drag-type tachometer. The system consists
of the following parts
Fig. Essential components of an Eddy-Current tachometer.
17
MEASUREMENT OF SPEED cont…
Electrical Tachometer
• The shaft drive a permanent
magnet inside an iron casing.
An aluminium cup is held close
to the rotating magnet
restrained by a control spring.
Now, when the magnet
rotates, eddy-current is set up
in the drag cup and a torque is
produced which tries to
oppose the field produced by
the eddy-current.
18