Lab 1- Fluid flowmeters (me) final | Flow Measurement | Fluid Dynamics

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We were also able to compare the three methods of flow measurement and could calibrate the rotameter, thus all the objec...

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Kian Hoe, Chua 2rd year BSc. Chemical Engineering University of New Brunswick Fredericton, New Brunswick. _______________________________________________________________________ _ Professor Cook, William Fluids Lab supervisor University of New Brunswick Fredericton, New Brunswick March 24th, 2007 Dear Dr. Cook: Attached is the laboratory report for the flow meters experiment. This experiment was conducted at the fluids lab on March 21st, 2007 under my leadership with my group members Emily Porter and Sarah Dwyer. Each team member was assigned a particular responsibility during the experiment and has also contributed to sections of this report. We have determined the loss coefficient and the variation of the loss coefficient with Reynolds number for the venturi and orifice meters. We were also able to compare the three methods of flow measurement and could calibrate the rotameter, thus all the objectives of this lab have been achieved. All the sections that are required have been included in this report. If you have any further questions, you can reach me at [email protected] .

Yours sincerely,

Kian Hoe, Chua

Encl: Report

ChE 2412- Chemical Engineering Laboratory I Fluid Mechanic Lab- Fluid Flowmeters

By Chua, Kian Hoe Porter, Emily Dwyer, Sarah

Abstract The goal of this experiment was to determine the loss coefficients for the venturi meter and orifice meter and to be able to establish the variation of the loss coefficient with the Reynolds number for both the venturi and orifice meter. The other objective was to calibrate the rotameter and to compare the three methods of flow measurement The flow rate through a pipe can be measured by using the orifice meter, venturi meter and the rotameter. From the energy equation, it can be deduced that when pressure head reduce, the velocity head will increase. In the orifice and venturi meters, the crosssectional area available for flow is restricted. Hence, an increase in velocity will result in a decrease in pressure at a point from continuity or energy equation. For rotameter, the same principle can be applied in this case. However, it should be noted that the area available for the flow is variable while the pressure drop across the restriction is keep constant. This can generally be achieved via a tapered tube and float arrangement. As flow increases, the flow raises until the dynamic force of the fluid balances the gravitational force acting on the float. The height of the float is directly related to the flow. From the results that we obtained, the venturi meter is closer to the value of the actual flow rate as compared to the orifice meter. This could be due to the fact that the venturi flow meter has a smaller head loss compared to the orifice meter by its design.

Test Method 1. The apparatus with the entire required dimension are sketched. The sketch is included in the appendix. 2. The pump is started in order to initiate the flow through the flow meters. 3. All the air from the piezometers is removed. 4. The reading of rotameter of about 27cm is set. This is then to be considered as a maximum flow. 5. The scale on the rotameter is read corresponding with the top of the rotameter float. 6. The temperature of the water in the reservoir is measured by using thermometer. 7. The condition of steady flow is achieved after a few minutes. The reading on of the head on point 1, 2, 5, and 6 is recorded. With this information, change in head can be obtained. This is then used to calculate the volumetric flow rate of the both the meters. 8. The time required in seconds for a certain amount of water to pass through the system is determined by using the built in balance system. Hence, the actual flow rate can be determined with this information. 9. The procedure above is the repeated by decreasing the reading on rotameter to 24cm, 18cm, 12cm, 8cm, 5cm, 3cm and 1cm to obtained a series of flow conditions.

Results and Discussion In order to determine the actual flow rate through the system a balance system was used. The time needed for 15 lb of water at 21.0ºC to flow into the balance was measured three times for each rotameter setting. This was accomplished using a 15 lb. weight and a stop watch. The average flow rate was then calculated using the following formula, Q=

m 1 ρ  ( t1 + t 2 + t 3 ) 3

Equation 1

Where Q = volume flow rate

(m s ) 3

 kg  3  m 

ρ = density 

m = mass (kg) ti = time (s) The following results were obtained;

(m s )

Table 1. Rotameter scale reading versus Actual Flow measured as the average of three trials.

Rotameter Reading (cm)

Average time for 15 lb. for water to flow through the system (s)

27 24 18 12 8 5 3 1

13.1633333 14.6033333 19.4266667 27.2166667 39.3333333 59.4633333 76.6166667 112.376667

Actual Flow Rate

3

0.00051803 0.000466948 0.000351012 0.000250545 0.000173364 0.000114676 8.90015E-05 6.06799E-05

These results are the actual flow rates that passed through each of the flow measuring devices in the system; the venture meter, the orifice meter and the rotameter. They will be used to find the calibration curve of the rotameter and to determine the correction coefficients for the Venturi meter and the Orifice meter.

In order to find the correction coefficients of the Venturi and Orifice meters the ideal flow through each must be calculated. The ideal flow equations omit flow losses caused by friction. The equation for ideal flow through a venturi meter and an orifice meter are equation 2 and equation 3 respectively.

Q = A2

Q = Ao

2 g ( h1 − h2 ) A 1 −  2   A1 

2

Equation 2

2 g ( h1 − h2 ) A 1 −  o   A1 

2

Where Q = the flow rate

Equation 3

(m s ) 3

Ao = the area of the circular Orifice meter (m2) A1 = the area upstream of the Venturi/Orifice meter (m2) A2 = the area at the throat of the Venturi meter (m2) h1 = the pressure head upstream of the Venturi meter (Pa) h2 = the pressure head at the throat of the Venturi meter (Pa) g = acceleration due to gravity

(m s ) 2

The results of these calcuations give the following results; Table 2. Ideal flow rates through Venturi and Orifice meters.

Rotameter Reading (cm)

Venturi meter 27 24 18 12 8 5 3 1

(m s )

Ideal Flow through a

0.000526 0.000465 0.000359 0.000263 0.000186 0.000127 9.6E-05 6.79E-05

3

(m s )

Ideal Flow through an Orifice meter

0.000833 0.000733 0.000558 0.000404 0.000293 0.000197 0.000153 8.82E-05

3

The Flow Coefficients for the actual flow of both the orifice meter and the venturi meter were calculated using their respective experimental values and the following formula: C= Q/ A2*(2g(h1-h2)/1-(A2/A1)²)^1/2 Where: C = flow coefficient Q= Actual Flow Rate (m^3/s) A2= The area of the approach pipe (m^2) A1 = The area of the orifice/venture opening (m^2) g = acceleration due to gravity (m/s^2) h1,h2 = pressure heads upstream and downstream of the meter The following results were observed; Table 3: Flow Coefficients for the Orifice and Venturi Meter Rotameter Flow Coefficient Reading (cm) Orifice meter 27 0.62224 24 0.63701 18 0.62891 12 0.61955 8 0.59233 5 0.58115 3 0.58229 1 0.68761

Flow Coefficient Venturi meter 0.38480 0.39190 0.38168 0.37221 0.36424 0.35269 0.36211 0.34914

In order to calculate Reynolds number, the following equation was being used; Re= VDρ/μ Where: Re = Reynolds Number

V = velocity in the approach pipe (m/s) ρ = Density of water at 21 °C (kg/m^3) μ = viscosity of water at 21 °C (Ns/m^2) The result for the approach Reynolds number was obtained as following; Table 4: Approach Reynolds Number for Orifice Meter (at 2in) Rotameter Reading (cm) Velocity (m/s) 27 1.33514 24 1.20348 18 0.90468 12 0.64574 8 0.44682 5 0.29556 3 0.22939 1 0.15639

Reynolds Number 68946.33 62147.69 46717.41 33345.87 23073.65 15262.57 11845.51 8076.08

Table 5: Approach Reynolds Number for Venturi Meter (at 1in) Rotameter Reading (cm) Velocity (m/s) 27 0.25555 24 0.23035 18 0.17316 12 0.12360 8 0.08552 5 0.05657 3 0.04391 1 0.02993

Reynolds Number 6598.38 5947.73 4471.00 3191.30 2208.22 1460.68 1133.65 772.91

From all the data obtained, the graphs of the meter against approach Reynolds number for the Venturi meter and the Orifice meter, and the calibration curve for the rotameter were being plotted as below;

Flow Coefficients vs. Reynolds Numbers for Orifice

Flow Coefficients

0.70 0.68 0.66 0.64 0.62 0.60 0.58 0.56 1000

10000 Approach Reynolds Number

Figure 1: Flow Coefficients versus Reynolds Numbers Plot for the Orifice Meter.

100000

Flow Coefficient

Flow Coefficient vs Reynolds Number for Venturi 0.395 0.390 0.385 0.380 0.375 0.370 0.365 0.360 0.355 0.350 0.345 0

2000

4000

6000

8000

Reynolds Number

Figure 2: Flow Coefficients versus Reynolds Number Plot for the Venturi Meter.

Rotameter Scale Reading (cm)

Rotameter Calibration 30 25 20 15 10 5 0 0

0.0001

0.0002

0.0003

0.0004

0.0005

0.0006

Actual Flow (m³/s)

Figure 3. Scale reading versus actual flow rate for the rotameter.

The venturi tube is considered to be most accurate when the Reynolds number is in the range of 105 or 106 according to the International Organization of standards. From the results we obtained; it is evident that the venturi meter is not as accurate as it could be based. However it is still determined to be the more accurate amongst the two meters on which the experiment was performed.

(LMNO, n.d)

High accuracy of orifice is resulted when the Reynolds number exceed 105. However, the Reynolds number as low as 4x103 are still valid. Hence, the Reynolds number we observed in the experiment for the orifice is in the acceptable range.

(LMNO.n.d)

Theoretically, the coefficient is supposed to decrease with decreasing Reynolds number. This is supposed to be due to the fact that at low Reynolds numbers, viscosity effects become significant. However, the desired results were probably not achieved due to the human error or faulty apparatus or even the combination of both. The calibration under different flow conditions is needed because this will result in different change in pressure and velocity. The velocity is significant in determining the Reynolds number since it is directly proportional to the Reynolds number. Conclusion From the experiment, the venturi meter is determined to be more accurate amongst the two due the fact that it gives a flow rate that is closer to the actual flow rate. The Reynolds number of orifice meter was determined to be within the acceptable range.

References

1. ChE 2412 laboratory manual, Department of Chemical Engineering, University of New Brunswick. 2. A supplementary text for Introductory Fluid mechanics by R.A Chaplin, University of New Brunswick.

3. LMNO Engineering, (n.d). Large Diameter Orifice Flowmeter Calculation for Liquid

Flow.

Retrieve

on

27

March

2007

from

http://www.lmnoeng.com/orifice.htm

Appendix Time (s) to get 15 lb of H2O Reading (cm) 27 24 18 12 8 5 3 1

1 13 14.93 19.34 27.4 39.21 57.8 77.78 111.6

2 13.05 14.87 19.69 26.93 39.13 58.59 77.1 112.25

3 13.44 14.01 19.25 27.32 39.66 62 74.97 113.28

997.8

conversion factor (kg/lb) =

ρH20 @ 21ºC(kg/m³)=

T ave (s) 13.1633333 14.6033333 19.4266667 27.2166667 39.3333333 59.4633333 76.6166667 112.376667

Actual Flow Rate (m³/s) 0.00051803 0.000466948 0.000351012 0.000250545 0.000173364 0.000114676 8.90015E-05 6.06799E-05

0.4536

Ideal Flow through the Venturi Meter Rotameter reading (cm) 27 24 18 12 8 5

d1 (in) 1 1 1 1 1 1

A1 (m²) 0.000507 0.000507 0.000507 0.000507 0.000507 0.000507

d2 (in) 0.625 0.625 0.625 0.625 0.625 0.625

A2 (m²) 0.000198 0.000198 0.000198 0.000198 0.000198 0.000198

(A2/A1)² 0.152588 0.152588 0.152588 0.152588 0.152588 0.152588

h1 (in H2O) 13 11.7 9.8 8.5 7.7 7.3

h2 (in H2O) 1 2.3 4.2 5.5 6.2 6.6

Δh (m) 0.3048 0.23876 0.14224 0.0762 0.0381 0.01778

Q (m³/s) 0.000526 0.000465 0.000359 0.000263 0.000186 0.000127

3 1

1 1

0.000507 0.000507

0.625 0.625

0.000198 0.000198

0.152588 0.152588

7.6 7.6

7.2 7.4

0.01016 0.00508

9.6E-05 6.79E-05

(A0/A1)² 0.036636 0.036636 0.036636 0.036636 0.036636 0.036636 0.036636 0.036636

h1 (in H2O) 12.1 10.9 9.2 8.1 7.5 7.2 7.5 7.5

h2 (in H2O) 3.2 4 5.2 6 6.4 6.7 7.2 7.4

Δh (m) 0.22606 0.17526 0.1016 0.05334 0.02794 0.0127 0.00762 0.00254

Q (m³/s) 0.000833 0.000733 0.000558 0.000404 0.000293 0.000197 0.000153 8.82E-05

Ideal Flow through the Orifice Meter Rotameter reading (cm) 27 24 18 12 8 5 3 1

d0 (in) 0.875 0.875 0.875 0.875 0.875 0.875 0.875 0.875

Approach Re for Orifice Meter (at 2in) Rotameter reading (cm) 27 24 18 12 8 5 3 1

A0 (m²) 0.000388 0.000388 0.000388 0.000388 0.000388 0.000388 0.000388 0.000388

d1 (in)

V (m/s) 0.410698 0.36162 0.275332 0.199497 0.144386 0.097345 0.075403 0.043534

2 2 2 2 2 2 2 2

A1 (m²) 0.002027 0.002027 0.002027 0.002027 0.002027 0.002027 0.002027 0.002027

Re 21208.42 18674.02 14218.16 10302.03 7456.064 5026.877 3893.802 2248.088

Approach Re for Venturi Meter at (1in) Rotameter reading (cm) V (m/s) Re 27 1.037695 26793.26 24 0.918424 23713.68 18 0.708881 18303.28 12 0.518847 13396.63 8 0.366881 9472.849 5 0.250627 6471.188 3 0.189456 4891.758 1 0.133966 3458.996 viscosity at 21ºC

Sample Calculation:

0.000982

Calculation of Actual flow rate for a rotameter reading of 27 cm: (15 lb )  0.4536 kg lb  3 m   Q= = = 0.000 518 m s 1 1 ρ  ( t1 + t 2 + t 3 )  997.8 kg 3  (13.00 s + 13.05 s + 13.44 s ) m  3   3 Calculation of ideal flow through a Venturi meter for a rotameter reading of 24 cm:

Q = A2

2 g ( h1 − h2 ) 1 −  A2   A1 

2

[(

)

 3.142  =  0.0254 m in ( 0.625 in ) 4   = 0.000 465 m

( ] 2

2 9.81 m

s2

)(11.7 inH O − 2.3 inH O) (0.0254 m in) 2

2

 0.625 in   1 −  1 in  

2

3

s

Calculation of ideal flow through an Orifice meter for a rotameter reading of 18 cm:

Q = Ao

2 g ( h1 − h2 ) A 1 −  o   A1 

[(

2

)

 3.142  =  0.0254 m in ( 0.875 in ) 4   = 0.000 558 m

( ] 2

2 9.81 m

3

s

Formula of Re for Orifice in excel =((E20*0.0254)*C43*'Actual Flow'!D15)/(C63) Formula of Re of Venturi in execel =((C7*0.0254)*C54*'Actual Flow'!D15)/(C63)

s2

)( 9.2 inH O − 5.2 inH O) (0.0254 m in) 2

 0.875 in   1 −  2 . 0 in  

2

2

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