Calibration of Hot Water Flow Meter

Calibration of Hot Water Flow meter

Greg Kirton

ENCH 435

11/24/03

Lab Partners: Phuong & Kevin

Professors: Dr. Jones & Dr. Henry Abstract

Team 3 was assigned to collect data to calibrate the hot water flow meter in the temperature system on Tuesday, November 11th. The following pages describe the configuration of the system, the equipment used to take measurements, the procedure for taking measurements and the results from our measurements.

From examining the measured flow rates and comparing them to the DAQ flow rates, we found the following equation appropriate for calibrating the DAQ flow rate.

Measured = 1.483x - 2.8274

Where x = data value from DAQ Table of Contents Introduction:

Team 3 has been working on calibrating the DAQ for the temperature system in

EMCS 120. This document will cover the calibration of the hot water flow meter and the procedure necessary for taking measurements and analyzing the data.

Figure 1. Diagram of the temperature system

Figure 1 is a schematic diagram of the temperature system showing the configuration that was used in our calibration. This particular configuration is counter- current; that means the hot water will flow through the heat exchanger in the opposite direction to the cold water. This configuration also shows the hot water on the tube side of the heat exchanger, and the cold water will flow through the shell side. This temperature system uses a shell & tube style heat exchanger. Figure 2 shows a shell & tube heat exchanger with labels that illustrate the tube side and shell side.

Shell Side (Cold water)

Tube Side (Hot water)

Figure 2. Illustrations of Tube and Shell Side in the HX Figure 3 shows the actual temperature system that we were working with.

Labeled are the locations of important elements of the temperature system.

Cold Water Hot HX DAQ Water Flow Flow meter meter

Figure 3. The Temperature System

In order to generate a calibration curve for the hot water flow rate, we must measure flow rate data for a variety of pump speed settings and compare the measured values to the DAQ values. The % pump motor speed will be our variable because the hot water flow rate depends on how fast the pump is operating. The operating range for which we will be collecting data is 30-100% pump speed. Theory:

For the flow rate calibration we ran the temperature system for 3 minutes but we waited 1 minute before taking measurements to ensure fewer transients in our measurements. Taking this approach enabled us to collect data that is more representative of the steady state flow rate and allows us to correlate our measure values with the DAQ values. Figure 5 shows a typical plot of the DAQ flow rate vs. time.

DAQ Hot Water Flow Rate vs. Time

8 ) n i m /

b 6 l (

l Steady State Region

0 0 1 2 3 Time (min)

Figure 5. DAQ vs. Time for hot water flow meter calibration

Equipment:

To calibrate the hot water flow rate we used a graduated cylinder, a stopwatch, and a hose. The hose was attached to the hot water exit; that allowed us to measure the flow rate of the hot water through the temperature system without system intrusion or major modifications. Procedure:

To begin taking hot water flow rate measurements one has to attach an additional hose to the hot water outlet. This method is used to avoid intrusion into the system, which would require disconnecting the existing plumbing and then re-soldering the pipe ends that were disconnected back together again. Figure 6 shows the location of the pipe in which the hot water exits and an additional hose is attached to take flow rate measurements.

Attach additional hose to the BOTTOM of this pipe

Figure 6. Location of Hot Water Exit

The procedure for taking hot water flow rate measurements is as follows. First set up the experiment to run for 3 minutes using a constant input. The constant input is the variable, which represents the % motor speed. We want this value to be constant for the experiment so we can correlate a measured flow rate to a DAQ flow rate at a given pump speed setting. We started our experiments using 30% pump speed and allowed the flow to reach steady state by waiting 1 minute before taking flow rate measurements.

When taking the measurements, we would allow the water to flow into the 1000 mL graduated cylinder for 10 seconds and then record the value. One person kept track of time, another person measured the amount of water that flowed into the graduated cylinder in 10 seconds, and another person recorded the data. This measurement was made 4 times for each % pump speed setting.

After taking 4 measurements at 30% pump speed, we increased the % pump speed by 10% until the data up to 100% is measured and recorded under the conditions described above.

The error for the DAQ was reported as 2 times the standard deviation. The error for the measured values was analyzed using the Student’s T formula that is given by the following equation.

Error = (Xmax - Xmin)*t/n

Xmax - Xmin = range of the measurements n = number of measurements t = "Student's t” (Refer to Table 1 for “t” values)

n t t/n

2 40.0 20.0

3 7.0 2.3

4 4.5 1.1

5 3.7 0.75

6 3.4 0.56 Table 1. Student’s T Values Results:

Table 2 shows the results from the measurements as well as the DAQ values for each of the experiments we ran (30-100% Pump speed)

% Pump Speed DAQ (lb/min) Error (2*STDEV) Measured (lb/min) Error (Students T) 30 3.66 0.15 2.45 0.15 40 3.78 0.17 2.93 0.36 50 4.21 0.08 3.52 0.15 60 4.74 0.12 4.12 0.07 70 5.40 0.11 5.11 0.00 80 6.33 0.22 6.61 0.15 90 2.51 0.02 7.72 0.22 100 2.57 0.02 8.63 0.15

Table 2. Results from Hot Water Flow Meter Calibration

Hot Water DAQ and Measured vs. Pump Speed 10 )

n 8 i m / b l 6 ( DAQ e t a

w Measured o l F 2

0 0 20 40 60 80 100 % Pump Speed

Figure 7. DAQ and Measured vs. % Pump Speed

The results are then plotted as DAQ and Measured vs. % Pump Speed. Figure 7 shows the plot of the results. In Figure 7 the DAQ appears to have lost all correlation to the measured data past 80% pump speed. So in our analysis we used only the points from

30%-80% pump speed to generate a calibration curve. Hot Water Flow Rate Calibration 10

y = 1.483x - 2.8274 R2 = 0.994 8 ) n i m

/ 6 b l (

d e r u s

a 4 e M

0 0 2 4 6 8 10 DAQ (lb/min)

Figure 8. DAQ vs. Measured

Figure 8 shows the DAQ values plotted against the measured values. Notice the

45o line that appears on the plot in Figure 8. Had the flow meter been properly calibrated already, the values for DAQ would be equal to the values for Measured, thereby producing a line with the slope y=x. However, this flow meter is not properly calibrated; therefore we must develop an equation that correlates the DAQ to the measured values.

The equation y = 1.483x - 2.8274 is our correlation equation:

x = DAQ flow rate value y = Calibrated flow rate value Conclusions:

The correlation equation is within the range of the error bars for measured and

DAQ data in Figure 8. Therefore, I conclude the equation y = 1.483x - 2.8274 to be an accurate calibration equation for hot water flow rate when pump speed is between 30%-

80%. To calibrate the flow meter, the following data should be input into the DAQ:

1.483 is the multiplier, this is equal to the slope of the best fit line and the offset is

-2.8274 this is equal to the y-intercept. Once these values are input into the DAQ, the

DAQ shall provide accurate flow rate data when the operating range is between 30-80% pump speeds.