3. Measurement

MEASUREMENT OF CHARACTERISTICS OF A FLOW-

THROUGH TYPE WATER BOILER

1 Aim of the measurement

Given a flow-through type boiler, the aim of the measurement is

to measure the heat-up curve (temperature change as a function of time) and

to determine its temperature rise and efficiency as a function of the flow rate.

2 Measurement of temperature

Many methods have been developed for measuring temperature. Most of these rely on

measuring some physical property of a working material that varies with temperature, e.g.:

glass thermometer

thermocouples

thermistors

bimetallic temperature gauge

2.1 Glass thermometer

One of the most common devices for measuring

temperature is the glass thermometer. This consists of a glass

tube filled with mercury or some other liquid, which acts as the

working fluid. Temperature increases cause the fluid to expand,

so the temperature can be determined by measuring the volume

of the fluid. Such thermometers are usually calibrated so that

one can read the temperature simply by observing the level of the

fluid in the thermometer.

2.2 Thermocouples

A thermocouple is a junction between two different metals

that produces a voltage related to a temperature difference. Any

junction of dissimilar metals will produce an electric potential

related to temperature. Thermocouples for practical measurement of

temperature are junctions of specific alloys which have a predictable and repeatable

relationship between temperature and voltage. Thermocouples are a widely used type of

temperature sensor for measurement and control and can also be used to convert heat into

electric power. They are inexpensive and interchangeable, are supplied fitted with standard

connectors, and can measure a wide range of temperatures. The main limitation is

accuracy: system errors of less than one degree Celsius can be difficult to achieve.

2.3 Thermistors

A thermistor is a type of resistor whose resistance varies

significantly with temperature. Thermistors are widely used as inrush

current limiters, temperature sensors, self-resetting overcurrent

protectors, and self-regulating heating elements. Thermistors typically

achieve a high precision within a limited temperature range [usually

−90°C to 130°C].

2.4 Bimetallic temperature gauge

A bimetallic strip can be used to convert a temperature change into mechanical

displacement. The strip consists of two strips of different metals which expand at different

rates as they are heated, usually steel and copper, or in some cases brass instead of copper.

The different expansions force the flat strip to bend one way if heated, and in the opposite

direction if cooled below its initial temperature. The metal with the higher coefficient of

thermal expansion is on the outer side of the curve when the strip is heated and on the

inner side when cooled.

A direct indicating dial thermometer (such as a patio thermometer or a meat

thermometer) uses a bimetallic strip wrapped into a coil. One end of the coil is fixed to the

housing of the device and the other drives an indicating needle. A bimetallic strip is also

used in a recording thermometer.

3 Description of the measuring equipment

The measuring equipment is the model of an electrically heated through-flow-type

boiler. Its sketch is shown in the Figure below.

The mass rate of flow of water m flowing through the instrument can be changed by

valve V. The electric heater H - which can be switched in two different power stages - warms

continuously the cold water flown in. The mass rate of flow can be measured on the

principle of volume meter tank (V, tVMT).

3.1 Theory and equations

The specific overall enthalpy of the entering water is 1

2

1

1

1

12

uv

ghp

eO

The specific overall enthalpy of the water at exit is 2

2

2

2

2

22

uv

ghp

eO

The change of overall enthalpy due to warming is

2

2

1

2

2

1212

12vv

hhguupp

eO

The internal energy of the entering water: 11

ctu

The internal energy of water at exit: 22

ctu

The difference of the internal energies: tcttcctctuuu 121222

The specific heat capacity of the water is Ckg

Jc

4187

After substituting the change of overall enthalpy we obtain

2

4187

2

1

2

2

12

12vv

hhgtCkg

Jppe

O

The following assumptions can be made:

( )

1 2

v v

thus, we have

Oe c t

The power-balance of the boiler - in steady state - is as follows:

envOelOPemPem

21 ,

where

m is the mass rate of flow, through the device, (kg/s)

e01 is the specific overall enthalpy of water entering the device, (J/kg)

e02 is specific overall enthalpy of water at exit (J/kg)

Pel is the power of heater, (W)

Penv is the power given to the environment, power loss, (W)

Upon rearranging, we obtain

el O env useful lossP m e P P P

i.e. the power of heater increases the overall enthalpy of the flowing water (useful power, Pu)

and another part leaves the system towards the environment.

3.2 The characteristic curve

After switching the device on the heating temperature T of the water increases but

after a certain time it will not change; it reaches its constant value t2 = Tconst. (t1 = T1 is the

entering temperature of the water). The constant value of the temperature difference

between the inlet and outlet is

1TTT

constconst

If the loss towards the surroundings is neglected, we have

Thus, for a given input electric power, the temperature rise is inversely proportional to

the mass flow rate:

4 The measuring exercise

a) The steps of the measurement are as follows:

i) Set a flow rate and keep it constant for the following steps.

ii) Measure the flow rate with the metering glass tube and stopwatch.

iii) Set the first heating power and wait until the output temperature stabilizes. Read

the output temperature.

iv) Set the second heating power and wait until the output temperature stabilizes.

Read the output temperature.

v) Go back to step i), set the next flow rate and repeat the measurement.

Draw the diagrams of Pel parameters with the measured points (4 flow rates for each

curve). The scales can be chosen optionally but suitably.

Given quantities:

deg25.0

deg141871000

3

AVccc

Ckg

Jc

m

kgIUP

Equations:

1TTT

t

VmIUcP

constconst

VMT

Pel

The heading of the measurement table

Serial

number

V

[dm3]

tVMT

[s]

m

[kg/s]

Tconst

[°C]

T1

[°C]

ΔTconst

[°C]

U’

[deg]

I’

[deg]

Pel

[kW]

5 Preparation questions

1. Describe 3 ways of measuring temperature.

2. Give the equations of the total enthalpy of the fluid before and after the boiler.

3. Assuming constant input power, describe the temperature rise-mass flow rate

relationship qualitatively.

4. Draw a sketch of the test rig.