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.

Liquid level can be measured by Direct methods: Dipstick For open tank an interval scale may be fitted, if convenient.

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.

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

Fig. Vented tank (u-tube fitted at bottom of the tank) 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)

Pa + ρgh + ρgy = Pa + ρmghm ρh = ρmhm – ρy 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:

Pressure method Cont… Also where

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.

Pressure method Cont…

Pressure method Cont… Pi + ρgh + ρgy1 + ρmghm = Pi + ρgh1 + ρgy2 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=h1, then And Substituting these values into above equation, we have

Pressure method Cont… Rearranging and making h term the subject Divide by density of measured liquid throughout and rearranging, we will have Also

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

Weight method cont… Force on the load cells is given by: Then mass content of the fluid Volume content = and the head (h) of the fluid,

Vmean = linear velocity 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. Mechanical Tachometer Centrifugal – force tachometer

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. 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)

MEASUREMENT OF SPEED cont… Electrical Tachometer An electrical tachometer consists of a transducer which converts rotational speed into an electrical signal coupled to an indicator. Eddy-current or drag-type tachometer. The system consists of the following parts Fig. Essential components of an Eddy-Current tachometer.

Electrical Tachometer 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.