University of Western Ontario Department of Chemical and Biochemical Engineering
CBE 2221 – Fluid Flow

Air Through Annubar
Performed: January 20th, 2011

Group members: Ashley Ching, Christopher Chai, Tanuj Dutta
Student no: 250523377
Date of submission: February 3rd, 2011

Table of Contents

Introduction 3 Theory and Nomenclature 3 Experimental Setup 3 Experimental Procedure 4 Results and Discussion 5 Conclusion and Recommendations 6 Citations and References 6 Appendix A…………………………………………………………………………………………………………..7 Appendix B 10

Introduction The objective of this lab is to calculate the mass flow rates across an annubar by measuring the pressure losses through the straight length of pipe and various fittings at different gas flow rates. The gas used in this experiment is air. The elbow meter was also calibrated and the fanning friction factor across the pipe was calculated. The friction loss due to the velocity head through the straight pipe and other fittings was also calculated.
Theory and Nomenclature To measure the gas flow in a pipe, an annubar is used. An annubar is a set of Pitot tubes mounted across a pipe. It measures the differential pressure between the static pressure and the full pressure of the stream. The Pitot tube’s full pressure chamber opening is facing against the stream so that is allows for conical aerodynamics. Applying Bernoulli’s principle and varying the pressure difference calculated the volumetric flow. The following equations were used to calculate the answer for the experimental objectives:
Mass flowrate is calculated using the calibration constant where is the mass flow rate (kg/s), ρ is density (kg/m3), and ΔP is the pressure drop in cm of water across the annubar. The velocity of the airflow in the pipe can be calculated as where u is the velocity (m/s), is the mass flow rate (kg/s), ρ is density (kg/m3), A is the inner cross-section area of the pipe (m2). It is important to note that the pipe has an inner diameter of 3.51 cm. Reynold’s number is needed to calculate the theoretical friction factor (f = 0.00114 + 0.125/Re0.32) and it’s equation is where ρ is density (kg/m3), u is the velocity (m/s), d is the internal diameter of the pipe (m), and μ is the viscosity of air at ambient temperature (which has a value of 2 x 10-5 Pa.s). The experimental fanning friction factor is calculated by f = ΔPd/(2 ρLu2) where ΔP is the pressure drop across (Pa), d is the internal diameter of the pipe (m), u is the air velocity (m/s), ρ is density (kg/m3), and L is the length of the straight pipe (m). For other fittings, the following equation can be used to calculate the friction constants K = 2 ΔP/ ρ u2. Lastly, the friction loss in terms of velocity in the straight and various fitting pipes was calculated by the equation ➢where h is the friction loss (m), K is the friction constant, u is the air velocity (m/s), and g is the gravitational acceleration (m/s2).

Experimental Setup
The apparatus that was used for this experiment consisted of a pressure regulator (Figure 1), an annubar (Figure 2), a long straight pipe, a 90 degree elbow, an elbow meter (corner tap), and finally a gate valve. Magnehelic pressure gages and manometers allowed for the measurement of the pressure drop across the previously listed devices. The apparatus was set up prior to the experiment as seen in Figure 4 below.

Figure 1 – Pressure Regulator

Figure 2 – Annubar with Magnehelic Pressure Gage

Figure 3 – Various Magnehelic Pressure Gages

Figure 4 - Air Flow System Set-Up
Experimental Procedure
Pressure was controlled by using the pressure regulator, while the flow rate of air through the system was controlled by using the gate valve. The first step of this experiment was to set the system air pressure to 2 psig by using the pressure regulator. The pressure drop across the annubar was adjusted to 0.2 inches of water. Both valves were used simultaneously to ensure that the pressure and air flow remained constant at 2 psig and 0.2 inches of water respectfully. The pressure drop across the straight pipe, corner tap, 90° elbow, 45° elbow and globe valve were recorded at 2 psig and 0.2 inches of water. The experiment was repeated at 2 psig with a pressure drop (inches of water) of 0.4, 0.6, 0.8 and 1. The experiment was repeated for various system pressures of 4, 6, 8, and 9 psig. At each of the different system pressures the pressure drop values across the annubar were recorded at 0.2, 0.4, 0.6, 0.8 and 1.
Results and Discussion In this lab one of the manipulated variables was the overall pressure (gauge) of the system. The gate valve was also used in conjuction with the pressure regulator to change the pressure drop across the Annubar. By using the pressure drop across the Annubar (in cm of water), the mass flow rate was found. Following this the velocity flow rate was calculated, and was used for calculating the fanning friction factor (for the straight pipe), friction constants and the friction loss in terms of heads (for all other valves and fittings). The Reynolds number of the flowing air was also calculated for the theoretical friction factor in the straight pipe. First off, there are a few trends that should be noted within the data itself. For each pressure set (2,4,6 PSIG etc) as the pressure drop across the annubar increased the mass flow rate and the velocity both increased. This resulted in an increasing Reynolds number. The data collected and tabulated at 2 PSIG seems to be the major outlier, as it did not follow the trends that occurred for the results at 4,6,8 and 9 PSIG. At each pressure, the Fanning Friction Factor (f) remained constant at 0.00756. Even though the Reynolds number was always increasing it seemed to be offset by the increasing airflow velocity, which in turn meant that the Fanning Friction Factor remained constant. Another important trend to note was that as the pressure drop across the Annubar dropped the experimental error of the Fanning Friction factor against it’s theoretical value kept increasing (the exception being at 2 PSIG). As the pressure drop increased with the increased flow rate, all of the friction constants for the fittings decreased. When the fluid has a lower velocity it can be considered to be more ‘viscous,’ meaning that it will have a greater friction constant. The friction constant equation has u^2 in the denominator meaning that the larger the velocity the lower the friction constant. Even though the friction constants were decreasing the overall friction loss in terms of velocity heads kept increasing as it was based heavily on the airflow velocity (u^2 in the numerator). The calibration constant of the elbow meter was also calculated for the 45o elbow meter. It was found to be 0.125. The calculation was only done once, as the value should remain constant. All sample calculations can be found in Appendix B. Friction constants for various fittings and valves in Perry’s Chemical Engineering Handbook can be found in Appendix A. The fittings that were compared were the 45o elbow, 90o elbow and the globe valve. The friction constants for the 45o elbow were ~0.235. The short 45o elbow has a constant equal to 0.35 and the long radius has a constant equal to 0.2 according the handbook. This either means that there was a large experimental error if the elbow was short radius or that there was a small error if it was a long radius elbow. It is also possible that the elbow used in the group’s lab set up was neither a standard or long radius elbow as defined by the handbook. The 90o elbow generally had a friction constant around ~0.235 also. No matter which value was used from the handbook there was a large error (minimum 50%) when comparing the values. Finally the globe valve had a friction constant that ranged from 5.88 to 4.94 (depending on the pressure drop across the annubar). In the handbook, an open Bevel seat and an open Composition seat Globe valve had friction constants around 6.0. Assuming the globe valve used in the lab set up were those, then the error was marginal. If they were not, then the error could have increased to 100%. Through the use of available formulas all of the lab objectives were completed.
Conclusion and Recommendations
In general this lab can be considered successful as all of the objectives of the lab were completed. Some of the trends that were noticed at high air pressures were not noticed at 2 PSIG. Even though all of the objectives were met, many of the friction constants that were calculated had fairly different values then those found in Perry’s Engineering Handbook. This may have occurred for a few reasons. It is possible that the lab results were simply not accurate enough. Another possibility is that the equipment used in the experiment were not exactly the same as the one’s that were used to calculate values in the handbook. One major error in this lab occurred when the pressure drop across the Annubar was above 0.6 inH20. At these higher pressure drops the actual gages became very hard to see, as the dial did not remain steady. The only real solution to this problem is through replacing the gage. Either replace it with a more accurate digital gage or with an analog scale that is larger and therefore increases in smaller increments. Another error in the lab occurred when reading the various gages. If the viewer did not look at the gage at the same horizontal level then it was very possible to read the gage incorrectly. This error was reduced because multiple were looking at the gages from different angles. Generally everyone agreed on the indicated pressure before it was recorded. In general the accuracy of the results could have been increased if more trials at each pressure were completed. Even considering these errors, many of the results varied greatly from their theoretical values. Even though the objectives of this lab were met, the validity of the lab results can be argued.
Citations and References http://www.control.com/thread/1009292469 Appendix A
Figure 1.1: Friction constants from Perry’s Chemical Engineering Handbook

Table 1 | | Important: | Area of Pipe= | 0.000968 | m^2 | Air pressure= | 2 | PSIG | Diameter = | 0.0351 | m | | Pressure drop (Inches of water) | Annubar | 0.2 | 0.4 | 0.6 | 0.8 | 1 | Straight Pipe | 0.06 | 0.1 | 0.16 | 0.2 | 0.24 | Corner tap (Elbow meter) | 0.14 | 0.26 | 0.38 | 0.5 | 0.6 | 90o Elbow | 0.04 | 0.08 | 0.12 | 0.16 | 0.2 | 45o Elbow | 0.04 | 0.08 | 0.11 | 0.14 | 0.18 | Globe Valve | 1 | 1.9 | 2.8 | 3.5 | 4.2 | | | | | | | Pressure Annubar (inH20) | 0.2 | 0.4 | 0.6 | 0.8 | 1 | Air Density (kg/m^3) | 1.39 | 1.39 | 1.39 | 1.39 | 1.39 | Mass Flow Rate (kg/s) | 0.0105 | 0.0148 | 0.0182 | 0.0210 | 0.0235 | Air Flow Velocity (m/s) | 7.81 | 11.04 | 13.53 | 15.62 | 17.46 | Reynolds Number | 19036.02 | 26920.99 | 32971.35 | 38072.03 | 42565.83 | Fanning Friction Factor f | 0.00227 | 0.00189 | 0.00202 | 0.00189 | 0.00181 | Theoretical f | 0.00648 | 0.00592 | 0.00562 | 0.00542 | 0.00527 | Friction Constant (Corner Tap) | 0.823 | 0.764 | 0.745 | 0.735 | 0.705 | Friction Constant 90 Elbow | 0.235 | 0.235 | 0.235 | 0.235 | 0.235 | Friction Constant 45 Elbow | 0.235 | 0.235 | 0.216 | 0.206 | 0.212 | Friction Constant Globe Valve | 5.88 | 5.58 | 5.49 | 5.14 | 4.94 | Friction Loss Corner Tap (m) | 2.56 | 4.75 | 6.94 | 9.14 | 10.97 | Friction Loss 90 Elbow (m) | 0.731 | 1.46 | 2.19 | 2.92 | 3.66 | Friction Loss 45 Elbow (m) | 0.731 | 1.46 | 2.01 | 2.56 | 3.29 | Friction Loss Globe Valve (m) | 18.3 | 34.72 | 51.17 | 63.96 | 76.76 | | | | | | | Table 2 | | | | | | Air pressure= | 4 | PSIG | | | | | Pressure drop (Inches of water) | Annubar | 0.2 | 0.4 | 0.6 | 0.8 | 1 | Straight Pipe | 0.06 | 0.1 | 0.16 | 0.2 | 0.24 | Corner tap (Elbow meter) | 0.14 | 0.26 | 0.38 | 0.5 | 0.6 | 90o Elbow | 0.04 | 0.08 | 0.12 | 0.16 | 0.2 | 45o Elbow | 0.04 | 0.08 | 0.11 | 0.14 | 0.18 | Globe Valve | 1 | 1.9 | 2.8 | 3.5 | 4.2 | | | | | | | Pressure Annubar (inH20) | 0.2 | 0.4 | 0.6 | 0.8 | 1 | Air Density | 1.55 | 1.55 | 1.55 | 1.55 | 1.55 | Mass Flow Rate | 0.0111 | 0.0157 | 0.0192 | 0.0222 | 0.0248 | Air Flow Velocity (m/s) | 7.39 | 10.45 | 12.80 | 14.77 | 16.52 | Reynolds Number | 20124.65 | 28460.56 | 34856.92 | 40249.31 | 45000.09 | Fanning Friction Factor f | 0.00756 | 0.00756 | 0.00756 | 0.00756 | 0.00756 | Theoretical f | 0.00639 | 0.00584 | 0.00554 | 0.00535 | 0.00520 | Friction Constant (Corner Tap) | 0.823 | 0.764 | 0.745 | 0.735 | 0.705 | Friction Constant 90 Elbow | 0.235 | 0.235 | 0.235 | 0.235 | 0.235 | Friction Constant 45 Elbow | 0.235 | 0.235 | 0.216 | 0.206 | 0.212 | Friction Constant Globe Valve | 5.88 | 5.58 | 5.49 | 5.14 | 4.94 | Friction Loss Corner Tap (m) | 2.29 | 4.25 | 6.21 | 8.18 | 9.81 | Friction Loss 90 Elbow (m) | 0.654 | 1.31 | 1.96 | 2.62 | 3.27 | Friction Loss 45 Elbow (m) | 0.654 | 1.31 | 1.80 | 2.29 | 2.94 | Friction Loss Globe Valve (m) | 16.4 | 31.1 | 45.8 | 57.2 | 68.7 | | | | | | | Table 3 | | | | | | Air pressure= | 6 | PSIG | | | | | Pressure drop (Inches of water) | Annubar | 0.2 | 0.4 | 0.6 | 0.8 | 1 | Straight Pipe | 0.06 | 0.1 | 0.16 | 0.2 | 0.24 | Corner tap (Elbow meter) | 0.14 | 0.26 | 0.38 | 0.5 | 0.6 | 90o Elbow | 0.04 | 0.08 | 0.12 | 0.16 | 0.2 | 45o Elbow | 0.04 | 0.08 | 0.11 | 0.14 | 0.18 | Globe Valve | 1 | 1.9 | 2.8 | 3.5 | 4.2 | | | | | | | Pressure Annubar (inH20) | 0.2 | 0.4 | 0.6 | 0.8 | 1 | Air Density | 1.72 | 1.72 | 1.72 | 1.72 | 1.72 | Mass Flow Rate | 0.0117 | 0.0165 | 0.0202 | 0.0233 | 0.0261 | Air Flow Velocity (m/s) | 7.03 | 9.94 | 12.17 | 14.05 | 15.71 | Reynolds Number | 21157.35 | 29921.01 | 36645.60 | 42314.70 | 47309.27 | Fanning Friction Factor f | 0.00756 | 0.00756 | 0.00756 | 0.00756 | 0.00756 | Theoretical f | 0.00631 | 0.00576 | 0.00547 | 0.00528 | 0.00513 | Friction Constant (Corner Tap) | 0.823 | 0.764 | 0.745 | 0.735 | 0.705 | Friction Constant 90 Elbow | 0.235 | 0.235 | 0.235 | 0.235 | 0.235 | Friction Constant 45 Elbow | 0.235 | 0.235 | 0.216 | 0.206 | 0.212 | Friction Constant Globe Valve | 5.88 | 5.58 | 5.49 | 5.14 | 4.94 | Friction Loss Corner Tap (m) | 2.07 | 3.85 | 5.62 | 7.40 | 8.88 | Friction Loss 90 Elbow (m) | 0.592 | 1.2 | 1.8 | 2.4 | 3.0 | Friction Loss 45 Elbow (m) | 0.592 | 1.2 | 1.6 | 2.1 | 2.7 | Friction Loss Globe Valve (m) | 14.8 | 28.1 | 41.4 | 51.8 | 62.1 | | | | | | | Table 4 | | | | | | Air pressure= | 8 | PSIG | | | | | Pressure drop (Inches of water) | Annubar | 0.2 | 0.4 | 0.6 | 0.8 | 1 | Straight Pipe | 0.06 | 0.1 | 0.16 | 0.2 | 0.24 | Corner tap (Elbow meter) | 0.14 | 0.26 | 0.38 | 0.5 | 0.6 | 90o Elbow | 0.04 | 0.08 | 0.12 | 0.16 | 0.2 | 45o Elbow | 0.04 | 0.08 | 0.11 | 0.14 | 0.18 | Globe Valve | 1 | 1.9 | 2.8 | 3.5 | 4.2 | | | | | | | Pressure Annubar (inH20) | 0.2 | 0.4 | 0.6 | 0.8 | 1 | Air Density | 1.88 | 1.88 | 1.88 | 1.88 | 1.88 | Mass Flow Rate | 0.0122 | 0.0173 | 0.0212 | 0.0244 | 0.0273 | Air Flow Velocity (m/s) | 6.71 | 9.50 | 11.63 | 13.43 | 15.01 | Reynolds Number | 22141.93 | 31313.42 | 38350.95 | 44283.87 | 49510.87 | Fanning Friction Factor f | 0.00756 | 0.00756 | 0.00756 | 0.00756 | 0.00756 | Theoretical f | 0.00623 | 0.00570 | 0.00541 | 0.00522 | 0.00508 | Friction Constant (Corner Tap) | 0.823 | 0.764 | 0.745 | 0.735 | 0.705 | Friction Constant 90 Elbow | 0.235 | 0.235 | 0.235 | 0.235 | 0.235 | Friction Constant 45 Elbow | 0.235 | 0.235 | 0.216 | 0.206 | 0.212 | Friction Constant Globe Valve | 5.88 | 5.58 | 5.49 | 5.14 | 4.94 | Friction Loss Corner Tap (m) | 1.89 | 3.51 | 5.13 | 6.75 | 8.10 | Friction Loss 90 Elbow (m) | 0.540 | 1.1 | 1.6 | 2.2 | 2.7 | Friction Loss 45 Elbow (m) | 0.540 | 1.1 | 1.5 | 1.9 | 2.4 | Friction Loss Globe Valve (m) | 13.5 | 25.7 | 37.8 | 47.3 | 56.7 | | | | | | | Table 5 | | | | | | Air pressure= | 9 | PSIG | | | | | Pressure drop (Inches of water) | | | | | Annubar | 0.2 | 0.4 | 0.6 | 0.8 | 1 | Straight Pipe | 0.06 | 0.1 | 0.16 | 0.2 | 0.24 | Corner tap (Elbow meter) | 0.14 | 0.26 | 0.38 | 0.5 | 0.6 | 90o Elbow | 0.04 | 0.08 | 0.12 | 0.16 | 0.2 | 45o Elbow | 0.04 | 0.08 | 0.11 | 0.14 | 0.18 | Globe Valve | 1 | 1.9 | 2.8 | 3.5 | 4.2 | | | | | | | Pressure Annubar (inH20) | 0.2 | 0.4 | 0.6 | 0.8 | 1 | Air Density | 1.96 | 1.96 | 1.96 | 1.96 | 1.96 | Mass Flow Rate | 0.0125 | 0.0176 | 0.0216 | 0.0250 | 0.0279 | Air Flow Velocity (m/s) | 6.57 | 9.30 | 11.38 | 13.15 | 14.70 | Reynolds Number | 22618.16 | 31986.91 | 39175.80 | 45236.32 | 50575.74 | Fanning Friction Factor f | 0.00756 | 0.00756 | 0.00756 | 0.00756 | 0.00756 | Theoretical f | 0.00620 | 0.00567 | 0.00538 | 0.00519 | 0.00505 | Friction Constant (Corner Tap) | 0.823 | 0.764 | 0.745 | 0.735 | 0.705 | Friction Constant 90 Elbow | 0.235 | 0.235 | 0.235 | 0.235 | 0.235 | Friction Constant 45 Elbow | 0.235 | 0.235 | 0.216 | 0.206 | 0.212 | Friction Constant Globe Valve | 5.88 | 5.58 | 5.49 | 5.14 | 4.94 | Friction Loss Corner Tap (m) | 1.81 | 3.37 | 4.92 | 6.47 | 7.77 | Friction Loss 90 Elbow (m) | 0.518 | 1.0 | 1.6 | 2.1 | 2.6 | Friction Loss 45 Elbow (m) | 0.518 | 1.0 | 1.4 | 1.8 | 2.3 | Friction Loss Globe Valve (m) | 12.9 | 24.6 | 36.2 | 45.3 | 54.4 |

Appendix B
Sample Calculations: