FLOW MEASURING APPARATUS
Group Members: Perera I. M. H. Pethum N. V. G. A. Raguram M. Randil O. P. C Rathnayake S. N. R. L.
130432E 130442J 130476P 130500L 130509X
Name : O. P. C. Randil Index no : 130500L Group : B2 Date of Assignment : 07.11.2014 Date of Initial submission : 21.11.2014 21.11.20 14
AIMS
Calculating the coefficient of discharge
Preparing the rating curves for Venturi meter and Orifice meter
Comparing Head losses
INTRODUCTION: Flow measuring apparatus designed to analyze typical methods of measuring the discharge of an incompressible fluid assuming low is under the steady-energy flow condition. (Bernoulli's flow condition.) Discharge is determined through a Venturi meter, Orifice plate meter and a Rota meter.
K Manometer tappings
A
26 mm
Venturi meter
B
16 mm
C
Wide angle Rota meter diffuser D
E
F
J G
20 mm 26 mm
51 mm Orifice meter
The shown above picture is a diagram of a f low measuring apparatus where water from hydraulic bench enters the equipment through a Perspex venture meter, which co nsists of a gradually converging short section, followed by a throat, and a long gradually diverging section. After a change in cross section through a rapidly diverging section, the flow continues along a plate with a hole of reduced diameter through which the fluid flows. Following a further setting length and a right angled bend, the flow enters the Rota meter. This consists of a transparent tube in which a float takes up an equilibrium position. The position of the float is a measure of the flow rate. After the Rota meter water returns via a control valve to the hydraulic bench and the weigh tank. The equipment has 9 pressure tappings as shown in the picture, each of which is connected to its own manometer for immediate read out.
THEORY: 1. Venturi meter
== == = + + 2 = + + 2 = 2[ + ] = 2[ ] → 1 = = → 2 = 2[ ] = 2 ∙ = = 2 Datum head Velocity Pressure Pressure Head Cross sectional area
A
B
== == =
Datum head Velocity Pressure Pressure Head Cross sectional area
Applying Bernoulli's equation between section A and B:
Compared to the pressure head and the v elocity head, datum head is negligible.
From equation of continuity,
From (1) & (2)
Substituting for the Head values and multiplying the whole equation by
, we can get
.
Compared to the theoretical value, the actual flow rate is lesser than it. Therefore actual flow rate represented in the following way, introducing a dimensionless constant called Co-efficient of discharge.
= 2 = 2 √ =
can be calculated from the gradient of the above graph.
Head loss across the Venturi meter: Inlet Kinetic energy:
2. Orifice Meter
== == =
Datum head Velocity Pressure Pressure Head Cross sectional area
E
F
== == =
Datum head Velocity Pressure Pressure Head Cross sectional area
Applying Bernoulli's equation between section E and F, by following the same procedure followed in the previous case, we can take,
= 2 == = Here,
consists of 2 factors.
Ratio of effective cross sectional area of flow at the contracted section to the actual cross section of the orifice. Ratio of actual velocity to ideal velocity to at the orifice.
0.83×
Head loss across the Orifice meter is In Orifice meter there is a slight increase of pressure head due to reflection of impact pressure from the orifice wall. Hence desired difference across the Orifice meter is less than that of measured.
∙
Inlet Kinetic Energy:
For comparison purposes, we can define a dimensionless parameter as follows.
= ℎ
APPARATUS: 1. Flow measuring apparatus
2. Measuring cylinder 3. Stop watch
PROCEDURE
The valve was opened to its maximum value and let the flow to approach a steady state. After the steady state is achieved, the relevant manometer readings of Venturi meter and Orifice meter are taken. While the reading were being taken, a specific volume of the fluid flow is measured, which was collected over a measured time period. Then the inlet valve was adjusted in a way the flow rate decreases and after settling to the steady state, another set of readings were taken while a specific volume flowed over a measured time period is collected. The above process is repeated until 6 sets of readings were taken.
CALCULATIONS: The actual flow rate is calculated based on the readings taken. 1. Venturi meter
×10 −
√ ×10−
80 76 76 76 20 2
2.83 2.76 2.76 2.76 1.41 0.45
− ×10 − 275.93 276.72 270.02 271.89 142.86 3.17
2. 0.525,8,525.20.28 = ..−.−. ×10− = 9.57×10− 2 = 9.57×10− == 0.0.0000531 0020 − − 9. 5 7×10 9. 5 7×10 = 2 = 0.0005310.000201 2×9. 81 0.000531 0.000201 = ..×× = 0.9 Graph pass through (0,0). Points taken to calculate the gradient are:
Gradient
1
9
2. Orifice meter
×10 − 124 128 130 130 -10 4
√ ×10− 3.52 3.58 3.61 3.61 0.45
− ×10 − 275.93 276.72 270.02 271.89 142.86 3.17
3. 0.604,,2429.9.22 = 23.29.00.249.642 ×10− = 7.63×10− 8 3 = 2×0. = 7.63×10− == 0.0.0000531 0020 − − 7. 6 3×10 7. 6 3×10 = 2 ×0.83 = 0.0005310.000201 2×9.81×0.83 0.000531 0.000201 − 7 . 6 3×10 = 8.76×10− = 0.87 Graph shoud pass through (0,0). Points taken to calculate the gradient are:
Hence the head loss through the orifice meter is less than measured,
1
3. Head loss Over kinetic head
= ℎ = = ( 2) For Venturi meter,
= 0.83× (161 ∙ 2) = 5.31×10− 1 ∙ − 2 16 − − − − ×10 ×10 ×10 ×10− ×102− For Orifice meter,
275.93 276.72 270.02 271.89 142.86 3.17
0.519 0.521 0.509 0.512 0.269 0.00597
80 76 76 76 20 2
124 128 130 130 -10 4
137.29 138.35 132.04 133.61 36.88 0.01816
5.827 5.493 5.756 5.688 5.423 1101.32
8.58 8.65 8.25 8.35 2.31 0.001135
119.95 122.28 130.79 129.22 29251.11
DISCUSSION: 1. Advantages and disadvantages of measuring flow using above methods.
Venturi meter
Advantages Especially suitable for measuring very small flow rates. Head loss is comparably less than orifice meters. Normally expected accuracy is high. (Variation of the read value about the true value is very low-about 1%) Not affected by the upstream flow turbulences or disturbances. Self-cleaning. The costs of installing and manufacturing are low. Good for measuring high flow rates. Requires a smaller length of the pipe for installation.
Disadvantages Installing and manufacturing costs are high. Viscosity effects are high. A larger length of the pipe is needed for installing the apparatus. Can accurately measure down to the 1/10 th of the maximum flow can be measured by the Venturi meter.
Orifice plates
Relative accuracy is low. (Compared with the Venturi meter.) Can accurately measure down to the ¼ th of the maximum flow can be measured by the orifice meter. High pressure loss in the orifice, makes the pumping costs go high. Viscous effects are high. Maintenance and changing the orifice plates are time consuming a lot.
2. Suggestions to improve the apparatus:
If a fluid bench is supplied instead of a tap, the uniformity of the flow rate is more assured. If another set of tapings are provided in the opposing direction of the apparatus, instead of a single measurement, a mean measurement could be obtained since most probably the water levels in the tubes are varying even in small distances. If the scaling is shown in the opposite side of the reading panel and if it's facilitated with a transparent strip to see the tube containing eac h tube through the scale, human errors done in reading could be reduced. If the apparatus is facilitated with a set of changeable Venturi meter sets and a set of Orifice plates are provided, the variation of the flow rate with the different parameters like the slope of the Venturi meter or the Orifice size can be measured. Since the laminar and turbulent flow types create a big change i n the variations of the flow rate patterns and the losses, it's better to have a method to identify the flow pattern like an ink injector. If a mechanical rotary type geared flow controller with an indicator can be introduced to the apparatus, the fluid flow rate could be measured very accurately than doing it manually.
3. If the Venturi meter was not horizontal, Then there should be a datum head difference as well than the other heads, so that could be included in the equation as well. The previously taken equation is shown here.
== == = + + 2 = + + 2 = 2[ + ] = = = 2[ + ] = 2 ∙ + = = 2 + Datum head Velocity Pressure Pressure Head Cross sectional area
A
B
== == =
Datum head Velocity Pressure Pressure Head Cross sectional area
Applying Bernoulli's equation between section A and B:
Here, the datum head is not negligible. Substituting from ,
Substituting for the Head values and multiplying the whole equation by
, we can get
.
Compared to the theoretical value, the actual flow rate is lesser than it. Therefore actual flow rate represented in the following way, introducing a dimensionless constant called Co-efficient of discharge.
= 2 + = 2 √ + Considering the log values,
ln = ln 2 + 12 ln +
4. The both graphs are exponentially vanishing graphs. However, the graph plotted for the orifice meter shows a more smooth variation than the graph for the Venturi meter. More area is covered under the graph plotted for orifice meter. Both graphs vanish when the flow rate (Inlet kinetic Energy) is at high values suggesting that the head loss over inlet kinetic energy ration is negligible at high rates of flow. In the low flow rates, the graphs can be analyzed using the area under each graph. In the graph, the area under the each graph shows the multiplication of the two variables plotted. That means the area under each graph shows the head loss of each fluid flow measuring equipment. We can clearly see that a greater amount of area is covered by the orifice meter than the venturi meter. This suggests that at a given low flow rate, the head loss made by the orifice meter is significant comparing to the head loss made by the Venturi meter. Therefore, at low f low rates, venturi meters are performing better than the orifice meters in measuring. Since the head values are m easured the tapings about the each measuring apparatus, we can say that at low flow rates, the measures given by the Venturi meter are more accurate and reliable than the measures given by the orifice meter. 5. According to Engineering Toolbox [1], there are many methods of measuring the flow rate. a. Rota meter (Variable area flow meter) b. Flow nozzles/ Sonic nozzles c. Velocity flow meters d. Pitot tubes e. Calorimetric flow meter f. Turbine flow meter g. Vortex flow meter h. Electromagnetic flow meter i. Ultrasonic Doppler flow meter j. Positive displacement flow meter k. Coriolis flow meter l. Mass flow meter m. Thermal flow meter n. Open channel flow meter
1. Engineering Toolbox 2014. Engineering Toolbox inc. [ONLINE] Available at: http://www.engineeringtoolbox.com/index.html [Accessed 16 November 2014]. 2. Learning Instrumentation And Control Engineering 2014. Instrumental toolbox . [ONLINE] Available at: http://www.instrumentationtoolbox.com/#axzz3JFsjcnvb[Accessed 16 November 2014]. 3. QED Environmental systems 2014. QED Environmental systems, Graco . [ONLINE] Available at: http://www.qedenv.com/ [Accessed 16 November 2014].
