In this study, a continuously mixing of a hot and cold water of a T-junction experiment will be used. Hot, cold and mixed stream flow rates and temperatures will be measured for five different hot cold -streams flow rates. The objectives of the experiment are 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 examine the accrual calibration equation of the orifice for hot, cold and mixed steam flow rate.
Theory
For any given non-reactive process at steady state, the general material and energy balances can be written as (Felder and Rousseau 2000):
∑▒m ̇_in -∑▒m ̇_out =0 (1)
Q ̇-W ̇=∑▒m ̇_out (h_out+〖V_out〗^2/2+gZ_out )-∑▒m ̇_in (h_in+〖V_in〗^2/2+gZ_in) (2)
In the present study, hot and cold-water streams are mixed at a T-junction to produce one mixed stream. Assuming, the hot and cold water streams are completely mixed at the T-junction, the system is a dichotic, no work done by or to the system, and potential energy changes are loses and that kinetic and potential energy changes are negligible, then Equations (1) and (2) can be reduced to
m ̇_(mix,pred)=m ̇_cold+m ̇_hot (3) (3)
m ̇_(mix,meas) h_mix=m ̇_cold h_cold+m ̇_hot h_hot (4)
where h is the enthalpy of each stream and can be defined as (Gengd and Boles, 1989)
h=C_p (T-T_0 ) (5)
whereT_0 is reference temperature and set to 0°C for each stream, cp is the heat capacity of the water and can be assumed to be constant.In the range the experiment is conducted. Combining Equation (4) and (5), the predicted mixed stream temperature can be calculated by
T_(mix,pred)=(m ̇_cold T_cold+m ̇_hot T_hot)/m ̇_(mix,meas) (6)
The predicted flow rate and temperature of mixed stream using Equation (3) and (6) are dependent upon measured Information of the streams before and after the T-junction. In order to determine which (if any) mass flow rate is wrong, Equation (3) and Equation (6) can be solved simultaneously to product the mixed stream temperature.
For example, if the mass flow rate of cold stream is assumed to be wrong, the temperature of the mixed stream can be predicted by replacing, the cold stream flow rate using Equation (3), to give following the predicted mixed stream temperature,
T_(pred,nom_cold )=((m ̇_(mix,meas)-m ̇_hot)T_cold+m ̇_hot T_hot)/m ̇_(mix,meas) (7)
Similarly, if the hot or mixed streams are assumed to be wrong, then the predicted mixed stream temperature can be calculated by:
T_(pred,nom_hot )=((m ̇_(mix,meas)-m ̇_cold ) T_hot+m ̇_cold T_cold)/m ̇_(mix,meas) (8)
T_(pred,nom_mix )=(m ̇_cold T_cold+m ̇_hot T_hot)/(m ̇_cold+m ̇_hot ) (9)
If one calibration equation is incorrect, however, the only one of the tree equations will actually predict the mixed stream temperature, which will agree with the measured value. And therefore, that flow rate missing in the equation is incorrect. The correct calibration equating can be determined by plotting correct mass flow rate as a function of the corresponding average volt readings of that stream.
Equipment
The schematic diagram of the experimented setup is shown in Figure 1. The entire flow loop is built using ½ inch nominal copper pipe and filling. The globe valves with pressure gauges used to control the flow rates of hot and cold water. Orifice meter and Rosemounddifferential pressurecell is used to measure the water flow rates.T-type thermocouples are used to measure the temperature of the water at various locations along the pipes. The OPTO 22 sub I/O system is used to convert the analog readings from thermocouples and DP/cells into digitals signals and the Labview(version 7.1) program is used to record and display the data.The calibration equations are given as:
