Electromagnetic flow meter
The flow rate of fluids that conduct electricity, such as water or molten metal, can be measured using an electromagnetic flowmeter whose principle of operation is based on the laws of electromagnetic induction. When a conductor of length L moves at right angles to a magnetic field of density B at a velocity v, an induced e.m.f. e is generated, given by: e = BLv. With the electromagnetic flow meter arrangement shown in Figure 23.11, the fluid is the conductor and the e.m.f. is detected by two electrodes placed across the diameter of the non-magnetic tube.
Thus with B and L known, when e is measured, the velocity of the fluid can be calculated.
Main advantages of electromagnetic flow meters
(i) Unlike other methods, there is nothing directly to impede the fluid flow.
(ii) There is a linear relationship between the fluid flow and the induced e.m.f.
(iii) Flow can be metered in either direction by using a centre-zero measuring instrument.
Applications of electromagnetic flow meters are found in the measurement of speeds of slurries, pastes and viscous liquids, and they are also widely used in the water production, supply and treatment industry.
Hot-wire anemometer
A simple hot-wire anemometer consists of a small piece of wire which is heated by an electric current and positioned in the air or gas stream whose velocity is to be measured. The stream passing the wire cools it, the rate of cooling being dependent on the flow velocity. In practice there are various ways in which this is achieved:
(i) If a constant current is passed through the wire, variation in flow results in a change of temperature of the wire and hence a change in resistance which may be measured by a Wheatstone bridge arrangement. The change in resistance may be related to fluid flow.
(ii) If the wire’s resistance, and hence temperature, is kept constant, a change in fluid flow results in a corresponding change in current which can be calibrated as an indication of the flow rate.
(iii) A thermocouple may be incorporated in the as- sembly, monitoring the hot wire and recording the temperature which is an indication of the air or gas velocity.
Advantages of the hot-wire anemometer
(a) Its size is small.
(b) It has great sensitivity.
Choice of flow meter
Problem 1. Choose the most appropriate fluid flow measuring device for the following circumstances:
(a) The most accurate, permanent installation for
measuring liquid flow rate.
(b) To determine the velocity of low-speed aircraft and ships.
(c) Accurate continuous volumetric measurement of crude petroleum products in a duct of 500 mm bore.
(d) To give a reasonable indication of the mean flow velocity, while maintaining a steady pressure difference on a hydraulic test rig.
(e) For an essentially constant flow rate with reasonable accuracy in a large pipe bore, with a cheap and simple installation.
(a) Venturimeter
(b) Pitot-static tube
(c) Turbine flow meter
(d) Float and tapered-tube flow meter
(e) Orifice plate.
Now try the following Practise Exercise
Practise Exercise 124 Further problems on the measurement of fluid flow
For the flow measurement devices listed 1 to 5, (a) describe briefly their construction (b) state their principle of operation (c) state their characteristics and limitations (d) state typical practical applications (e) discuss their advantages and disadvantages.
1. Orifice plate
2. Venturimeter
3. Pitot-static tube
4. Float and tapered-tube meter
5. Turbine flowmeter.
Equation of continuity
The calibrations of many of the flow meters described earlier are based on the equation of continuity and Bernoulli’s equation.
The equation of continuity states that for the steady flow of a fluid through a pipe of varying cross-section the rate of mass entering the pipe must be equal to the rate of mass leaving the pipe; this is really a statement of the principle of conservation of mass. Thus, for an incompressible fluid:
a1 v1 = a2 v2
where a1 = cross-sectional area at section 1, a2 = cross-sectional area at section 2, v1 = velocity of fluid at section 1, and v2 = velocity of fluid at section 2