Calibration of a Venturi Flowmeter

Group 4

Supervised by Dr Tian

Nick Taylor __________________ (signed)

Iain Howard __________________ (signed)

Andrew Hardman __________________ (signed)

Xu Yang __________________ (signed)

School of Mechanical and Systems Engineering: Stage 1

Abstract

Flow Meter Calibration is a process to verify the flow rate of a system within industry. The flow rate is

known to be dependent on the pressure difference across a restricted and unrestricted piping. The

objective of this test is to familiarise flow meter calibration using a Venturi system and also determine the

relationship between the flow rate and the pressure difference when measured using a manometer. This

will allow a formula to be used to calculate a given flow rate.

An experimental test in which both the degree of height difference ( and Flow Rate (Q) are measured

using an Armfield F1-15 Bernoulli’s Thereom Demonstration Unit which suggests that the relationship

could be in the form of:

here the m in e alue is oun to e

m = 0.598 (uncertainty range of 0.5397 to 0.6718)

The value of m = 0.598 fell outside actual known value of m ≈ 0.5. The value was used to calculate the K

value which was found to be:

K = 0.0004 ±0.00005

Where:

Q = 0.0004 · H0.598

It was shown that the hypothesised equation of Q=K·Hm to be an appropriate formula to be used for Flow

Meter cali ration. As long as uncertainties where calculate an known limitations o Bernoulli’s Thereom

were considered.

Contents

List of Notations

1. Introduction

1.1 Background

1.2 Objectives

2 Theory

3 Apparatus & Method

4 Results

4.1 Data Uncertainties

5 Discussion

6 Conclusion

List Of Notations

V = Volume Unit: m3

H1 = Height at “a” Manometer Tu e Unit: m

H2 = Height at “e” Manometer Tu e Unit: m

∆H = Height difference (H1 – H2) Unit: m

Q = Volumetric Flow Rate Unit:

T = Time Unit: secs

k = Correctional Co-efficient Unit:

m = Arbitrary power

1. Introduction

1.1 Background

In differing industries there is a need to have a specific flow rate to be used as part of a system. To be

able to achieve this, calibration of the system will be needed. Flow meter calibration can be verified

using many differing systems. In our testing we will be using a Venturi system.

The Venturi system is ase on low continuity an The Bernoulli’s Thereom.

Included in the test will be familiarisation with using a Venturi system with connected manometers and

also analysising the resulting data.

Ha ing con ucte the test it will allow a iscussion on the results an also o Bernoulli’s Theorem.

1.2 Objectives

Correct procedural use of a Venturi System,

Show that experimental data justifies using a calibration formula of ,

Whilst including choice of a single best fixed value of the index value m whilst taking

into account estimate uncertainties an the theoretical alue o m ≈ 0.5, an

Quantifying the correction co-efficent, including its uncertainties to establish

accuracy of the test.

2. Theory

For a Volumetric Flow Rate measurement using a Venturi system, it should be possible to plot the

resulting data of Q vs ∆H and suggest that a power law formula would fit a trendline. To be able to

easily show this, plotting Ln (Q) vs Ln (∆H) would then give a linear trendline.

If this was shown to be true, then the resulting gradient of the line would indicate the relevant power

involved which would be unknown at the time.

This would then suggest:

If it is decided that the above is an acceptable function, then it would be necessary to identify a

correctional co-efficient (K).

To find the value of k, plotting Q vs should generate a graph with a straight trendline. The gradient

of the trendline would give the respective K value.

Once all the values are known comparison for its practical use of the system could be evaluated when

comparing the function with the well documented equation for Flow Meter calibration testing of:

However this would have to be critiqued as physical assumptions may not hold true for the particular

apparatus used in the testing and also uncertainties identified within the procedure.

3. Apparatus & Method

Apparatus which was used to conduct the calibration comprised of an Armfield F1-15 Bernoulli’s

Thereom Demonstration Unit (See figure 3.1) fitted on to an Armfield F1-10 Hydraulics Bench (See

figure 3.2).

Figure 3.1 Armfield F1-15 Bernoulli’s Figure 3.2 Arm iel F1-10 Hydraulics Bench

Thereom Demonstration Unit

Calibration also required a 1000ml measuring container and a Stopwatch.

The actual test section comprises of a Venturi system (figure 3.3) with a flow regulator inlet valve and

an outlet valve. The Venturi system has 8 tappings connected to a manometer bank which incorporates

a manifold with air bleed valve.

For the purpose of the calibration, only the manometer tubes from tappings “a” an “e” are nee e or

the actual height readings.

A flow chart diagram (figure 3.4) shows the full system of the calibration.

Figure 3.3 Venturi System specifications

Figure 3.4 Flow system for calibration

Method

Firstly ensure there is an uninterrupted water flow going to the hydraulics bench.

Next Open both the Inlet and Outlet valve slowly and allow the fluid in the manometer tubes to

stabilise.

Slowly a just the al es as to ma imise the amount o lui in the “a” tu e an minimise the

lui in the “e” tu e.

Take readings of the actual heights for both manometers. The board is in 10mm increments, use

a Engineering rule with 1 mm increments for added accuracy of the readings.

Next use the 1000ml measuring container to measure the water flow from the test rig for 5

secs.

Note the amount of water in the container.

Repeat the pre ious 4 steps a urther 4 times, each time re ucing the height le el in the “a”

tu e an increasing the height le el in the “e” tu e, until on the inal reading there is minimal

height i erence in the rea ings rom oth the “a” an “e” manometer tu es.

There will now be 5 data sets for which it will be possible to compile results and compute the relevant

data.

4. Results

Measure alues or the Volume an heights or Manometers attache to tappings “a” an “e”.

Volume (m3) Time (sec) H1 (metres) H2 (metres)

ΔH (metres) Q (mᵌ/s)

9.05E-04 5 0.287 0 0.287 1.81E-04

8.35E-04 5 0.273 0.018 0.255 1.67E-04

7.70E-04 5 0.248 0.039 0.209 1.54E-04

5.00E-04 5 0.196 0.085 0.111 1.00E-04

3.10E-04 5 0.158 0.12 0.038 6.20E-05

6.80E-05 5 0.139 0.135 0.004 1.36E-05

The ΔH and Q were calculated as such:

Calculated log values of the Flow Rate (Q) and the Height difference (ΔH)

LnH

LnQ

-1.248273063

-8.617013527

-1.366491734

-8.697516746

-1.565421027

-8.778557956

-2.198225078

-9.210340372

-3.270169119

-9.688376173

-5.521460918

-11.20544077

Figure 4.1 Graph showing relationship between Ln(H) and Ln(Q)

y = 0.5983x - 7.8535

y = 0.6718x - 7.7054

y = 0.5397x - 8.0163

-12

-11.5

-11

-10.5

-10

-9.5

-9

-8.5

-8

-7 -6 -5 -4 -3 -2 -1 0

Ln(Q

)

Ln(H)

Scatter Graph showing relationship between Ln(H) and Ln(Q)

Figure 4.2 Graph showing relationship between flow rate (Q) and Height Di erence^0.598 (∆H^m)

y = 0.0004x + 3E-06

y = 0.0004x - 5E-06

y = 0.0003x + 4E-06

0

0.00005

0.0001

0.00015

0.0002

0.00025

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Flo

w R

ate

(Q

), m

^3/s

Height Difference^0.598 (∆H^m)

Scatter Graph showing relationship between flow rate (Q) and Height Difference^0.598 (∆H^m)

4.1 Data Uncertainties

Volume: ±0.000010m3

Time: ±0.31 sec (total) Includes ±0.30 sec human reaction + ±0.01 sec Stopwatch accuracy

H1: ±0.001m

H2: ±0.001m

∆H: ±0.002m

Q: [

]

Ln Q: (

)

Ln Q: (

)

Volume (m3)

V Uncertainty

Time (sec)

T Uncertainty

H1 (metres)

H1 Uncertainty

H2 (metres)

H2 Uncertainty

ΔH (metres)

ΔH Uncertainty

9.05E-04 1.10E-02 5 6.20E-02 0.287 3.48E-03 0 0.00E+00 0.287 6.97E-03

8.35E-04 1.20E-02 5 6.20E-02 0.273 3.66E-03 0.018 5.56E-02 0.255 7.84E-03

7.70E-04 1.30E-02 5 6.20E-02 0.248 4.03E-03 0.039 2.56E-02 0.209 9.57E-03

5.00E-04 2.00E-02 5 6.20E-02 0.196 5.10E-03 0.085 1.18E-02 0.111 1.80E-02

3.10E-04 3.23E-02 5 6.20E-02 0.158 6.33E-03 0.12 8.33E-03 0.038 5.26E-02

6.80E-05 1.47E-01 5 6.20E-02 0.139 7.19E-03 0.135 7.41E-03 0.004 5.00E-01

Q (mᵌ/s) Q Uncertainty LnH Ln(H)

Uncertainty LnQ

Ln(Q) Uncertainty

1.81E-04 1.32E-05 -1.248273063 6.97E-03 -8.617013527 7.30E-02

1.67E-04 1.24E-05 -1.366491734 7.84E-03 -8.697516746 7.40E-02

1.54E-04 1.15E-05 -1.565421027 9.57E-03 -8.778557956 7.50E-02

1.00E-04 8.20E-06 -2.198225078 1.80E-02 -9.210340372 8.20E-02

6.20E-05 5.84E-06 -3.270169119 5.26E-02 -9.688376173 9.43E-02

1.36E-05 2.84E-06 -5.521460918 5.00E-01 -11.20544077 2.09E-01

5. Discussion

The objectives in principle were all met. Correct use of the equipment was learnt, including removing

an air u le rom the manometer tu e or tapping “a”.

When the resulting data for Ln (Q) and Ln (H) were plotted (Figure 4.1), it can be clearly seen that the

relationship is linear. This allowed a calculation of the gradient which resulted in a value of m as 0.598.

Including the uncertainties in the value this was midway in the range of 0.5397 and 0.6718.

Unfortunately the value was quite outside an appropriate accuracy for industry when taking into

account the theoretical value of 0.5.

The K value showed 0.0004 ±0.00005 which is an accuracy of ±12.5%. As with above this well above an

accuracy norm of ±2%.

The equipment manufacturer of the Armfield F1-15 Bernoulli’s Thereom Demonstration Unit o la el

the unit as for educational and demonstration purposes. The test also assumed that the equipment

was set up to the manu acturer’s gui elines.

Furthermore there are limitations to Bernoulli’s Theorem which coul help in icate as to why we

reached the m and k values.

Limitation of Bernoulli's Equation:-

Shear stress of a liquid means the velocity of the liquid gradually decreases towards the walls of the

pipe ue to riction. In Bernoulli’s equation only the mean elocity is use an losses ue to the shear

stress are neglected.

If the liquid has a turbulent flow some Kinetic Energy is converted into Heat Energy and in a Viscous

Flow some Energy is lost due to Shear Forces. Thus while using Bernoulli's Equation all such losses

should be neglected, which does not happen in actual practise.

The equation neglects external forces which could have a real world effect on the fluid velocity.

6. Conclusion

Theoretically it has been shown that test data shows that the hypothesised equation of Q=K·Hm to be an

appropriate formula to be used for Flow Meter calibration. When uncertainties were evaluated for both

the K and m values it showed that there was insufficient accuracy that the test would meet stringent

industry standards.

However the Venturi System is a recognised calibration method for Flow Meters. In the discussion areas

have been identified to show how the inaccuracies possibly have accrued during the test and the

limitations o Bernoulli’s Theorem itsel . The test rig itself is not of a design for industry calibration ideals

and is more suited for theoretical demonstration purposes.

As a whole the experiment did allow for the tabulated data to be plotted to find equivalent linear

trendlines when Ln Q vs Ln H were plotted. Also there was sufficiently linearity in from the plotting of Q vs

Hm.