MEASUREMENTS AND

INSTRUMENTATION

LIQUID LEVEL AND QUANTITY MEASUREMENT

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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.

Liquid level can be measured by

1) Direct methods:i. Dipstick• For open tank an interval scale may be

fitted, if convenient.

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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.

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2) Indirect Methods:

i. 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

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Types of floats used are:• Hollow metal spheres• Disc and• Ceramic floats

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.

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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)

Pressure method Cont…A level Z-ZL.H.S Pressure = R.H.S Pressure

Pa + ρgh + ρgy = Pa + ρmghm

ρh = ρmhm – ρyWhen the mercury levels were initially at the same height as the

base of the tank, Then:

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2

2

2

mmm

mmm

m

hhh

hhh

hy

Pressure method Cont…

• Also where

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mm hh

2

1

mhkh

2

1

mK

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.

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Pressure method Cont…

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Pressure method Cont…

At level Z-Z

LHS Pressure = RHS pressure

Pi + ρgh + ρgy1 + ρmghm = Pi + ρgh1 + ρgy2

ρh + ρy1 + ρmhm = ρh1 + ρy2

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Since the mercury levels are both yo below the tank bottom when h=h1, then And

Substituting these values into above equation, we have

21m

o

hyy

22m

o

hyy

22 1m

ommm

o

hyhh

hyh

Pressure method Cont…

Rearranging and making h term the subject

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22 1m

ommm

o

hyhh

hyh

mmmm h

hhhh

221

mmm hhhh 1Divide by density of measured liquid throughout and rearranging, we will have

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mmhhh Also

1,

m

m kwherehKh

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

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Weight method cont…

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Force on the load cells is given by:

Then mass content of the fluid

Volume content =

AhgMgF

g

FAhm

gFAh

and the head (h) of the fluid,

AgFh

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 = linear velocity

ωmean = angular velocity

• However, the instantaneous linear or angular velocity is of greater interest, and this may be measured in several ways.

1. Mechanical Tachometer2. Centrifugal – force tachometer

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tS

tQ

MEASUREMENT OF SPEED cont…Mechanical tachometer

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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.

Centripetal force = Ma = It can measure speed up to 40,000 R.P.M and are usually used to make and break circuit for speed control (governor)

r

Mv 2

MEASUREMENT OF SPEED cont…Electrical Tachometero 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

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.

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MEASUREMENT OF SPEED cont…