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Air Flow Measurement

Chemical Engineering Practice

Fluid flow is an important consideration in the field of chemical engineering as it is a popular method for the transportation of chemicals within a plant. Most fluid flow problems can be solved using the Bernouli equation, (P/ + gz + v 2/2) = F dw/dm. The Bernouli equation can be solved very easily when all the parameters are known. However, friction factors often have to be experimentally arrived at. In the pilot plant there is a long vertical pipe with an unknown friction factor which was experimentally determined and correlated to several semi empirical equations. This was accomplished by first arriving at the average velocity within the pipe using a Pitot tube and several barometers. The air was forced through the pipe using a blower with various volumetric flow rates to obtain data points. In addition to this the pipe is fitted with an orifice meter at the far end. The discharge coefficient was measured for this at various flow rates. This was accomplished by using the average velocity determined in the first part of the experiment to predict the flow through the orifice meter along with the pressure drop that was directly measured. Please find a copy of the report attached to this document.

Equipment The cylindrical pipe located in the pilot plant at the University of Ottawa is a 3 internal diameter pipe. It is equipped with a blower at one end and an orifice plat at the over end. There is a barometer attached to the pipe 2 from the blower, a Pitot tube 188 further along the pipe and another barometer 56.6 further from the Pitot tube. Just past

the last barometer there is an orifice plate with a diameter of 1.8 and another barometer to measure the pressure drop across it. The blower was turned on and its damper was fully opened to get a maximum flow rate of air through the pipe. The pressure just above the blower was measured along with the pressure of the free steam at the Pitot tube. The Pitot tube was placed at the center of the pipe and the stagnation pressure was recorded. The Pitot tube was moved to 10 positions, 5 on either side of the center of the pipe, to obtain a pressure distribution within the pipe. The pressure drop across the orifice was noted as well. The Pitot tube was placed again in the center and the damper was adjusted to obtain a lower pressure reading. Pressures of 80%, 70%, 60%, 50% and 40% of the initial pressure were used to repeat the process. At the end of the experiment the temperature of the room was measured to be 23 C.

Summary of Results The average velocity was determined to be 5.13 m/s with the damper completely open. Table 1, shows the average velocity in relation to the reduction of pressure measured from the Pitot tube at the center of the pipe. Table 1: Average velocity within the pipe Pressure %of initial (Pitot tube) average velocity (m/s) 100% 5.13 80% 4.53 70% 4.28 60% 3.98 50% 3.72 40% 3.17

Using the average velocity along with the pressure drop across the orifice meter the discharge coefficients were determine have an average 0.63. The discharge

coefficients do not appear to have much correlation with the average velocity, Table 2. Table 2: Discharge coefficient for various flow rates average velocity m/s Discharge coefficient 5.13 0.63 4.53 0.64 4.28 0.65 3.98 0.63 3.72 0.64 3.17 0.61

Finally, the friction factor of the pipe was determined to be approximately 0.006 in most cases. The friction, f, appeared to be relatively constant through the experimental conditions despite the fact the Reynolds number and pressure drops across the pipe were different, table 3. Table 3: Friction factor for various Reynolds numbers and pressure drops Pressure Drop (Pa) Re f 31 24 23 21 20 15 2.61E+04 2.31E+04 2.18E+04 2.03E+04 1.90E+04 1.62E+04 0.006 0.006 0.006 0.007 0.007 0.008

Discussion
The Pitot tube used in this experiment was a static Pitot tube. This apparatus measured the pressure of the free steam, P o, fluid and the pressure required to stop a small cross sectional area of the fluid from moving; referred to as the stagnation pressure, P s. Performing a Bernouli balance across the Pitot tube will yield the velocity of the fluid if one neglects friction and changes in elevation shown as follows: (P/ + gz + v2/2) = F dw/dm F = 0, dw/dm = 0 , z1 = z2 = 0 (P/ + v2/2) = 0 (Ps Po)/ = vo2/2 vs2/2, vs = 0 vo = (2(Ps Po)/ )1/2 equation 13

The advantage of Pitot tube is that it is a very simple and inexpensive method of assessing the velocity in a pipe. However, a Pitot tube does present some difficulties in its use; mainly that it measures the local velocity within a pipe, not the average velocity. This comes about by the no slip condition of the fluid at the fluid pipe interface. This results in a velocity profile that must be measured in order to obtain the average velocity. In a laminar flow regime this is relatively simple; however, in turbulent flow several different points must be measured. The flow was assumed to be turbulent prior to performing the experiment; a decision as to the actual flow regime could only be made after completing the experiment. The Pitot tube was placed at 5 positions of either side of the center of the pipe. These positions were selected such that they have an equal contribution to the average 5

velocity. This was accomplished by dividing the pipe into 5 equal subareas and then positioning the Pitot tube at the center of the area. The average velocity could then be solved by taking a simple average of the velocities. These positions were measured on either side of the center of the pipe. A more complex method of solving the velocity within the pipe would be equation 2 which does not assume incompressible flow. Typically, gas flow rates less than 0.3 of the Mach number, 100 m/s, can be assumed to be incompressible 2. The velocities of air that were arrived at were in the order of 1 to 5 m/s. As such, this did not necessitate the used of equation 2. v = ( 2/( 1- ) * (/ o) ((Ps/Po) /( 1- ) 1))1/2 equation 23 With the velocities obtained it was then possible to calculate the Reynolds number, the ratio of shear to viscous forces of the fluid. The Reynolds numbers that were calculated were all in excess of 4000; which indicated that all the velocities used in this experiment were all in the turbulent flow regime. If the Pitot tube was not positioned such that each velocity gave had an equal weight contribution to the overall average velocity a curve could have been fitted to the data. Performing a surface integral upon the velocity as the function of the radius would have yielded the volumetric flow rate. The volumetric flow rate could then be divided by the area to given an average velocity. Using the velocity again, it was possible to solve for the discharge coefficient from the orifice meter; this was done using equation 3. The discharge coefficients obtained appeared to not be a function of the velocity as the average discharge coefficient was 0.63. This is in agreement with previous literature 1 values as the coefficients all tend

towards 0.63 when the Reynolds number is in excess of 10 4 for turbulent flow. Although, some of the individual values werent in complete agreement, they were relatively close and the variation may be the result of experimental error shown in figure 1 of appendix 1. The friction factors were obtained from experimental results by using the pressure drop and the average velocity. These results were plotted against two semi empirical correlations for friction factor, equations 3 and 4. These equations are used to correlate the Reynolds number to the friction factor for smooth pipe in a turbulent flow regime. f = 0.046*Re-0.2 f = 0.0014 + 0.125*Re-0.32 Equation 33 Equation 43

The experimental results appear to be in good agreement with the values predicted by the equations shown in figure 2 in appendix 1. All three trend lines appear to decrease with increasing Reynolds numbers. This suggests that the data obtained from the lab is of a good quality and that the pipe can be characterized as smooth. A hydraulically smooth pipes friction factor can be obtained by von Krmn equation, equation 5. Plotting the friction factors and product of the product friction factors and the Reynolds numbers as a semi log plot yielded a linear plot from which the parameters of the von Krmn could be obtained. A linear trend line was fit to the data and reading off the slope gave the experimentally arrived of values of 6.49 for the slope and 24.499 for the intercept shown in figure 3 in appendix 1. This suggests that the pipe used in this experiment is not hydraulically smooth as equation 5 does not appear to fit the data remotely. 1 / (f/2) = 2.5ln(Re *(f/8)) + 1.75 equation 53

Since the pipe can not be characterized as hydraulically smooth the relative roughness needed to be estimated. Using the Moody chart1, the relative roughness of the

pipe, /D, appears to be 0.000001. The curve on the Moody chart for this value is labeled as Smooth Pipes and appears to predict the calculated friction factors well.

Conclusions and Recommendations

The experiment was a success; the velocity profile through a smooth pipe was measured with varying Reynolds numbers. Additionally, a friction factor was

successfully calculated for each average velocity and compared to several semi empirical correlations. The two different methods for calculating the friction factor gave very similar results as seen when graphed, Figure 3. The discharge coefficient was determined to have an average value of 0.63. If this experiment were repeated again it could be improved by some minor modifications to the apparatus. A better damper could be installed on the air inlet to better restrict the airflow entering the pipe. As it stands, it was not possible to obtain a reading for 20% and 10% pressure of stagnation versus that measured with the damper open when the Pitot tube was positioned in the center of the pipe. Another method to improve the experiment would be to install more accurate pressure barometers on the pipe. The pressures measured at all points along the pipe oscillated around a central value which suggests a large uncertainty in these measured value.

Appendix 1 Graphs

Orifice Meter
0.66 0.65 0.65 0.64 0.64 0.63 0.63 0.62 0.62 0.61 1.40E+04

Discharge Coefficient

2.05E+04

2.70E+04

Reynolds Number

Friction Factor Plot

-2.000 4.100 -2.050 -2.100 -2.150 -2.200 -2.250 -2.300

4.300

4.500

Reynolds Number

Figure 2: Comparison of friction factors for two semi empirical correlations

von Krmn plot 19 18.5 18 (f/2)^-0.5 17.5 17 16.5 16 15.5 6.15 6.2 6.25 6.3 6.35 6.4 6.45 6.5 6.55 6.6 y = 6.492x - 24.299 R = 0.7841
2

ln(Re*(f/8)^0.5)

Figure 3: Ploting of friction factors in such a fashion to obtain the parameters for the von Krmn equation

Appendix 2 Sample Calculations

1) Velocity at 1.423 inches & 100% u = [2(Ps P0)/] u = [(2*0.010 KPa*1000 Pa)/1.19 kg/m3] u = 4.10 m/s 2) Average Velocity at 100% uavg = (All velocities except velocity at center)/10 uavg = (4.10 + 4.85 + 5.18 ++ 4.10) m/s/10 uavg = 5.13 m/s 3) Reynolds Number Re = (uavg*D*)/ Re = (5.13 m/s*0.0762 m*1.19 kg/m3)/1.78x10-8 Pa-s Re = 2.61x104 4) Discharge Coefficient Co = (uavg*(32/1.82)*[1-(1.8/3)4])/(2000*Porifice/) Co = (5.13 m/s*(32/1.82)*[1-(1.8/3)4])/(2000 Pa*0.266 KPa/1.19 kg/m3) Co = 0.63 5) Friction Factor = (Ps*1000*D)/(*u2avg*L) = (0.031KPa*1000 Pa*0.0762 m)/(1.19 kg/m3*(5.13m/s)2*(6.21m)2) = 0.006 10

6) Log Reynolds Number Log(Re) = Log(2.61x104) Log(Re) = 4.417 7) Log Friction Factor Log() = Log(0.006) Log() = -2.217 8) Log Equation 14 Log() = Log(0.046*Re-0.2) Log() = Log(0.046*(2.61x104)-0.2) Log() = -2.221 9) Log Equation 15 Log() = Log[0.0014+(0.125/Re0.32)] Log() = Log[0.0014+(0.125/(2.61x104)0.32)] Log() = -2.206 10) von Krmn Equation 1/(/2) = 1/(0.006/2) ln[Re(/8)] = ln[2.61x104(0.006/8)] 1/(/2) = 18.15 ln[Re(/8)] = 6.58

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