Table 4. The measured and predicted stream temperatures and their associatederrors for five
steady state runs.
Run Tmix2,meas
(°C) Tpre,mix
(°C) Tpre,nomhot
(°C) Tpre,nomcold
(°C) Tpre,nommix
(°C)
1(7-38) 36.0±0.9 45.3±4.0 26.4±2.3 37.0±1.7 33.0±1.0
2(61-77) 35.3±0.8 42.4±3.1 24.5±2.3 34.6±1.2 31.3±1.0
3(84-104) 35.9±0.7 42.7±4.0 26.6±2.4 35.7±1.8 32.4±1.1
4(120-141) 37.3±0.6 43.9±3.7 30.4±2.0 38.1±1.7 34.8±0.9
5(190-210) 36.8±0.7 43.7±3.9 28.8±2.3 37.2±1.7 33.8±1.0
Figure 5 shows the corrected cold steam flow rates versuscorresponding square root of prime drop recording in volts. The corrected cold steam calibration equation was obtained by using a linear regression between the corrected mcoldand corresponding drop recording. The corrected calibration equation of equation (10) should be
m ̇_cold=103.67√(V_cold ) (13)
Figure 4. Corrected mass flow rate as a function of the square root of the corresponding volt
readings
When the mixed steam temperature was predicted, the heat capacity, Cp, of water was assumed to be constant. The highest temperature is 51.5 degree Celsius and the lowest temperature is 22.1 degree Celsius. From Chemical property Handbook(1999), the heat capacities at those temperatures were found to be75.62 J/(molK)and 75.14 J/(molK). The difference is quite small and can be ignored. Therefore, assuming Cp being constant is a valid assumption.
Conclusions
The experiment wasa simple mixing of hot and cold water at a T-junction. The objectives of the experiment were to investigate the optimum thermocouple location after the T-junction, to use mass and energy balance equations to predict mass flow rates and temperature of the mixed stream after the T-junction and then compare these with the measured values and to investigate the accuracy of the calibration equation.
In the experiment, the temperature given by the thermocouple located at 6 cm from the T-junction, Tmix1, was found to have a higher temperature and standard deviation than the values given by the thermocouples located at 23 and 40 cm from the T-junction (Tmix2 and Tmix3). The values and standard deviations of Tmix2 and Tmix3 were similar. It means the two streams are not completely mixed at a distance of 6 cm downstream of the T-junction and therefore, theoptimum thermocouple should be placed at a minimum of 23 cm from the T-junction. Using mass and energy balances, the predicted mixture stream flow rates and temperatures were calculated for five runs. The predicted values, Mmix,predicted, did not agree within errors with the measured values, Mmix,meas, sincecalibration equations are incorrect. When the temperature was predicted without values produced by the calibration equation for the orifice meter for the cold stream, it was found that predicted temperature agreed within experimental error with the measured value. Therefore the initial calibration equation for the cold stream flow rate is incorrect andthe correct calibration equation of cold water mass flow rate should be:
m ̇_cold=103.67√(V_cold )
Nomenclature
Q ̇_ Heat Flow (W)
W ̇_ Work (W)
m ̇_ Mass flow rate, kg/s