Table 2.The measured hot, cold and mixed stream flow rates as well as the predicted mixed
stream flow rate and their associated errors.

Run Mc (kg/h) Mh (kg/h) Mmix,meas(kg/h) Mmix,pred(kg/h)
1(7-38) 155.0±7.6 97.2±5.6 183.2±9.4 252.1±9.5
2(61-77) 252.4±13.4 139.6±6.5 287.6±15.5 392.1±15.0
3(84-104) 286.9±17.4 171.5±14.1 340.4±21.4 458.5±22.
4(120-141) 302.9±17.8 211.2±14.9 390.1±23.9 514.2±23.3
5(190-210) 363.4±26.8 239.7±18.0 451.6±31.9 603.0±31.3

During the experiment, three thermocouples are used to determine the temperature of three different locations after the T-junction. Table 3 shows a comparison the measured hot, cold and mixed stream temperatures and their associated errors and standard deviations.The mixed steam temperature is measured at 6cm (Tmix1), 23cm(Tmix2) and 40cm(Tmix3) after the T-junction.The errors of the temperatures were calculated by assuming±0.3°Cthermocouple accuracy and plus twice the standard deviation. As shown in Table 3, it can be observed that the temperature of the mixed stream 1 is higher than the other two and the standard deviations of Tmix1 are higher than the other two. Tmix2do agree with the Tmix3within their errors but Tmix1do not agree with the rest temperatures. Therefore, it can be assumed that, in the first thermocouple which is 6 cm away from the T-junction, the streams are not completely mixed. Compare the temperatures at second thermocouple and third thermocouple, the temperatures are almost the same, and the standard deviations are also not big changes. Thus, it can be assumed that the streams are completely mixed at the second and third place. The optimum thermocouple should be located at the position of second one which is 23cm after the T-junction.

Table 3.The measured mixed stream temperatures and theirassociated errors and standard
deviations.

Run Tmix1 (°C) Tmix2 (°C) Tmix3 (°C)
1(7-38) 38.5±2.9 36.0±0.9 35.4±0.8
δ 1.3 0.3 0.3
2(61-77) 37.0±2.1 35.3±0.8 34.6±0.5
δ 0.9 0.2 0.1
3(84-104) 38.0±2.5 35.9±0.7 35.2±0.7
δ 1.1 0.2 0.2
4(120-141) 39.5±1.8 37.3±0.6 36.5±0.7
δ 0.7 0.1 0.2
5(190-210) 38.9±1.9 36.8±0.7 36.0±0.6
δ 0.8 0.2 0.1

Table 4 compares the measured and predicted stream temperatures and their associatederrors for five steady state runs.The temperatures of Tmix2 are measured by thermocouple. The predicted temperatures for the mixed streams are calculated by Equation (6). Then, by assuming the calibration equation (10) is wrong. The predicted temperature, Tpre,nomcold, can be calculated by equation (7). By assuming the calibration equation (11) is wrong, The predicted temperature, Tpre,nomhot, can be calculated by equation (8). By assuming the calibration equation (12) is wrong,the predicted temperature, Tpre,nommix, can be calculated by equation (9). The error of predicted mixed stream temperatures can be calculated using the technique by Holman (2001). From the table, it is clear that the Tmix2,meas and Tpre,nomcold have the similar value. For example, on the run 1, the Tpre,nomcold is 37.0±1.7°C and the Tmix2,measis 36.0±0.9°C.  They do agree within their errors. But Tpre,nomhot, Tpre,mixand Tpre,nommix are quite different from Tmix2,meas. Based on the assumptions made before,  the value of Tpre,nomcold is calculated without the value of mc. Therefore, the mass flow rate of cold water is wrong and the calibration Equation (10) is not accurate.