1 UNIVERSITI TENAGA NASIONAL
COLLEGE OF ENGINEERING
DEPARTMENT OF MECHANICAL ENGINEERING
MESB333
ENGINEERING MEASUREMENT LAB SEMESTER 1, 2014/2015
TITLE : DETERMINING FLUID VELOCITY AND DISCHARGE COEFFICIENT
AUTHOR : TUNKU ATIQAH BINTI TENGKU HAMNET
SECTION : 3A GROUP : B
GROUP MEMBERS:
FAIQAH BINTI MOHD FADZIL ME089856
SOFEA BALQIS BINTI JUB,LI ME090241
RUCGNES A/L APPARAO ME090233
MOHAMAD AIMAN B. TALIT ME088598
INSTRUCTOR :
DATE PERFORMED : 23 JUNE 2014 DATE SUBMITTED : 30 JUNE 2014
TABLE OF CONTENT
EXPERIMENT I: DETERMINING FLUID VELOCITY
Summary / Abstract 3
Objective 3
Theory 3-5
Equipment 6
Procedure 6-7
Data, Observation and Results 8-10
Analysis and Discussion 10
Conclusion 11
EXPERIMENT II: DETERMINATION OF DISCHARGE COEFFICIENT
Summary / Abstract 12
Objective 12
Theory 12-13
Equipment 14
Procedure 14
Data, Observation and Results 15-18
Analysis and Discussion 19
3 SUMMARY/ABSTRACT
SUMMARY/ABSTRACT
It is extensively used to verify the airspeed of an airplane, water speed of a boat, and to measure liquid, air and gas velocities in industrial applications. The pitot tube is used to evaluate the local velocity at a given position in the flow stream and not the average velocity in the pipe or conduit. The Bernoulli equation is then practical to calculate the velocity from the pressure difference.
or (1)
When fluid flows through a immobile solid wall, the shear stress set up near to this boundary due to the relative motion between the fluid and the wall directs to the growth of a flow boundary layer. The boundary layer may be either laminar or turbulent in nature depending on the flow Reynolds number.
The growth of this boundary layer can be discovered by examining the velocity profiles at selected cross-sections, the core region still outside the border layer showing up as an area of more or less consistent velocity.
If velocity profiles for cross-sections different remoteness from the pipe opening are compared, the pace of growth of the boundary layer along the pipe length can be determined. Once the boundary layer has mature to the point where it fills the whole pipe cross-section this is termed "fully developed pipe flow".
OBJECTIVE
1) To learn the method of measuring airflow velocity using pitot tube.
2) To understand the working principle of pitot tube as well as the importance of Bernoulli equation in deriving and calculating the velocity.
THEORY
A pitot tube is used to explore the developing boundary layer in the entry length of a pipe which has air drawn through it. With pitot tube, the velocity distribution profiles can be determined at a number of cross-sections at different locations along a pipe. With pitot tube, air flow velocities in the pipe can be obtained by first measuring the pressure difference of the moving air in the pipe at two points, where one of the points is at static
velocity. The Bernoulli equation is then applied to calculate the velocity from the pressure difference. v 2p or 2gh' (1)
p – The pressure difference between the pitot tube and the wall pressure tapping measured using manometer bank provided (
g
x where x is the level of fluid used in the manometer).
h’ – the pressure difference expressed as a 'head' of the fluid being measured (air) The air density at the atmospheric pressure and temperture of that day.(kg/m3) g gravitational acceleration constant (9.81 m/s2)
When fluid flows past a stationary solid wall, the shear stress set up close to this boundary due to the relative motion between the fluid and the wall leads to the development of a flow boundary layer. The boundary layer may be either laminar or turbulent in nature depending on the flow Reynolds number.
The growth of this boundary layer can be revealed by studying the velocity profiles at selected cross-sections, the core region still outside the boundary layer showing up as an area of more or less uniform velocity.
If velocity profiles for cross-sections different distances from the pipe entrance are compared, the rate of growth of the boundary layer along the pipe length can be
determined. Once the boundary layer has grown to the point where it fills the whole pipe cross-section this is termed "fully developed pipe flow".
Reynolds Number
The Reynolds number is a measure of the way in which a moving fluid encounters an obstacle. It's proportional to the fluid's density, the size of the obstacle, and the fluid's speed, and inversely proportional to the fluid's viscosity (viscosity is the measure of a fluid's "thickness"--for example, honey has a much larger viscosity than water does).
Revd : fluid density v : fluid velocity d : obstacle size
5 A small Reynolds number refers to a flow in which the fluid has a low density so that it responds easily to forces, encounters a small obstacle, moves slowly, or has a large viscosity to keep it organized. In such a situation, the fluid is able to get around the obstacle smoothly in what is known as "laminar flow." You can describe such laminar flow as dominated by the fluid's viscosity--it's tendency to move smoothly together as a cohesive material.
A large Reynolds number refers to a flow in which the fluid has a large density so that it doesn't respond easily to forces, encounters a large obstacle, moves rapidly, or has too small a viscosity to keep it organized. In such a situation, the fluid can't get around the obstacle without breaking up into turbulent swirls and eddies. You can describe such turbulent flow as dominated by the fluid's inertia--the tendency of each portion of fluid to follow a path determined by its own momentum.
The transition from laminar to turbulent flow, critcal flow, occurs at a particular range of Reynolds number (usually around 2500). Below this range, the flow is normally laminar; above it, the flow is normally turbulent.
Calculation of Airflow Velocity
The manometer tube liquid levels must be used to calculate pressure differences, Dh and pressure heads in all these experiments. Starting with the basic equation of hydrostatics: p =
gh (2)
we can follow this procedure through using the following definitions: Example:
Manometer tubes 1(static ‘pressure’*) 2(stagnation ‘pressure’) Liquid surface readings
(mm)
X1 X2
Angle of inclination,
=0
equivalent vertical separation of liquid levels in manometer tubes,
h = (x1 - x2)cos
(3)
If rk is the density of the kerosene in the manometer, the equivalent pressure difference
p is: p = k g h = k g(x1 - x2) cos (4)
The value for kerosene is rk = 787 kg/m3 and g = 9.81 m/s2. If x1 and x2 are read in mm, then: p = 7.72(x1 - x2)cos [N/m2] (5) The
p obtained is then used in second equation (1) to obtain the velocity.
To use the first equation (1), convert this into a 'head' of air, h’. Assuming a value of 1.2 kg/m3 for this gives:
h' k air (x1x2) 1000 cos [N/m 2 ] (6) APPARATUS
7 PROCEDURE
a) Five mounting positions are provided for the pitot tube assembly. These are: 54 mm, 294 mm, 774 mm, 1574 mm and 2534 mm from the pipe inlet
b) Ensure that the standard inlet nozzle is fitted for this experiment and that the orifice plate is removed from the pipe break line.
c) Set the manometer such that the inclined position is at 00.
d) Mount the pitot tube assembly at position 1 (at 54mm, nearest to the pipe inlet). Note that the connecting tube, the pressure tapping at the outer end of the assembly, is
connected to a convenient manometer tube. Make sure that the tip, the L-shape metal tube of the pitot tube is facing the incoming flow.
e) Note that there is a pipe wall static pressure tapping near to the position where the pitot tube assembly is placed. The static pressure tapping is connected to a manometer tube.
f) Position the pitot tube with the traverse poisition of 0mm. Start the fan with the outlet throttle opened.
g) Starting with the traverse position at 0mm, where the tip is touching the bottom of the pipe, read and record both manometer tube levels of the wall static and the pitot tube until the traveverse position touching the top of the pipe.
h) Repeat the velocity traverse for the same air flow value at the next positon with the pitot tube assembly. Make sure that the blanking plugs is placed at the holes that are not in use.
DATA, OBSERVATION AND RESULTS
Data Sheet for Velocity Measurement Using Pitot Tube Traverse
Position (mm)
Pitot Tube at 54 mm Static ‘Pressure’ Reading
117 mm
Pitot Tube at 294 mm Static ‘Pressure’ Reading
120 mm Stagnation ‘Pressure’ Reading (mm) x (mm) p (N/m2) Velocity (m/s) Stagnation ‘Pressure’ Reading (mm) x (mm) p (N/m2) Velocity (m/s) 0 100 17 131.24 14.79 100 20 154.4 16.05 10 98 19 146.68 15.64 99 21 162.12 16.45 20 97 20 154.4 16.05 98 22 169.84 16.83 30 96 21 162.12 16.45 97 23 177.56 17.21 40 95 22 169.84 16.83 96 24 185.28 17.58 50 95 22 169.84 16.83 96 24 185.28 17.58 60 95 22 169.84 16.83 97.5 22.5 173.7 17.02 70 95 22 169.84 16.83 102 18 138.96 15.23 Traverse Position (mm) Pitot Tube at 774 mm Static ‘Pressure’ Reading
126 mm
Pitot Tube at 1574 mm Static ‘Pressure’ Reading
130 mm Stagnation ‘Pressure’ Reading (mm) x (mm) p (N/m2) Velocity (m/s) Stagnation ‘Pressure’ Reading (mm) x (mm) p (N/m2) Velocity (m/s) 0 102 24 185.28 17.58 116 14 108.08 13.43 10 104 22 169.84 16.83 114 16 123.52 14.36 20 98 28 216.16 18.99 112 18 138.96 15.23 30 97 29 223.88 19.33 110 20 154.4 16.05 40 96 30 231.6 19.66 100 30 231.6 19.66 50 98 28 216.16 18.99 99 31 239.32 19.98 60 100 26 200.72 18.29 98 32 247.64 20.30 70 106 20 154.4 16.05 110 20 154.4 16.05
9 Pitot Tube at 2534 mm
Static ‘Pressure’ Reading 136 mm Traverse Position (mm) Stagnation ‘Pressure’ Reading (mm) x (mm) p (N/m2) Velocity (m/s) 0 121 15 115.8 13.89 10 112 24 185.28 17.58 20 110 26 200.72 18.29 30 108 28 216.16 18.99 40 110 26 200.72 18.29 50 106 30 231.6 19.66 60 108 28 216.16 18.99 70 116 20 154.4 16.05 Sample Calculation Taking :- Pitot tube = 54mm
Static pressure reading = 117mm At transverse position = 0m
Stagnation pressure reading is 100mm ∆x = static pressure, x1 - stagnation pressure, x2 = 117mm - 100mm = 17mm ∆p = 7.72 (∆x) cos where = 0o , cos 0o = 1 = 7.72 (17mm) = 131.24 N/m2 Velocity, V = 2p /P√ = 2(131.24) /1.2 = 14.79 m/s
Graph 1: Velocity against Traverse Position
ANALYSIS AND DISCUSSION
1. From the data collected, we have plotted the graph of velocity against transverse position. The velocity of the Pitot Tube can be expressed as sinusoidal position or look like the Simple Harmonic Motion (SHM) of its corresponding transverse position. Pitot tube of 2534 mm have the best symmetrical sinusoidal shape where as pitot tube of 54 mm have unsymmetrical sinusoidal shape.
2. While conduction this experiment, there are lots of possible errors that has resulted in the inaccuracy of the results obtained. Among the sources of error is parallax error during the process of taking the value of manometer. The
manometer level fluctuates at a very high and inconsistent rate making it hard to collect the accurate reading. This error can be said as the main source of error as the value of manometer that taken influences the results of the experiment.
CONCLUSION
The objective of the experiment is achieved. The principle fluid (air) velocity measurement is explored and understood. The understanding on how to compute
parameters such as ∆x, ∆p and the velocity with the help from the data obtained from the experiment is enhanced. 0 5 10 15 20 25 0 20 40 60 80 V el ocit y (m /s) Traverse Position (mm)
Velocity against Traverse Position
54mm 294mm 774mm 1574mm 2534mm
11 SUMMARY/ABSTRACT
An orifice plate meter shapes a precise and economical device for measuring the discharge for the flow of liquids or gases through a pipe. The orifice presented can be put into the suction pipe at the flanged joint about half way along its length. The multi-tube manometer given is used to determine the pressure fall across the orifice and this is associated to the discharge determined independently.
In this experiment, we are going to find out the discharge coefficient by conducting an experiment for an orifice plate in an airflow pipe. Also using the static pressure tapings given, we are determining the pressure distribution along the pipe downstream of the orifice plate. From the obtained CD of the orifice plate, we will determine the CD of a small nozzle.
OBJECTIVE
This experiment will ask student to determine the discharge coefficients, CD for orifice plate and the small nozzle.
THEORY
The orifice plate meter forms a jet, which expands to fill the whole pipe, some diameter distance downstream. The pressure difference between the two sides of the plate is related to the jet velocity, and therefore the discharge, by the energy equation: Q = Ajvj = AoCcvj = AoCcCv
2gh
where,
Q – discharge (volume/time) _
Aj – jet cross-section area at minimun contraction (vena contracta) Ao – orifice cross-2/4: d = orifice size)
vj – jet velocity at minimum contraction (vena contracta) Cc coefficient of contraction of jet
Cv coefficient of velocity of jet
g – gravitational acceleration (9.81 ms -2)
These two coefficients are normally combined to give a single coefficient of discharge: CD = Cc.Cv Equation (1) now becomes
Q = CDAO
2gh (2)
If Q can be determined independently, then the discharge coefficient can be determined as follows:-
CD =
Q
Ao 2gh (3)
Values of Qi can be determined if the standard nozzle is fitted at the pipe inlet. Qi = C’DAi
2ghi (4)
If hi = the drop in pressure head across the inlet, the discharge = (
k/
air )* (xbeforenozzle –xafternozzle):
in which Ai = standard nozzle cross-section area (= pi*d2 /4) and C’D assumed to be 0.97. Values of hI are obtained from the manometer tube levels connected to the pipe inlet pressure tapping and open to the atmosphere.
Calculating the CD of orifice plate:
From equation (4), with the Qi obtained from standard nozzle where CD of standard nozzle is assumed to be 0.97, we can calculate the CD of orifice plate. Assuming that Qi across standard nozzle and Qo across orifice plate is the same, apply equation (3)
CD = Qo Ao 2gho (5) where ho – ( k/
air)*( x across orifice)
13 APPARATUS
PROCEDURE
(a) Insert the orifice plate in position (taking care to observe the instructions as to) in which the surface should face the approaching airflow.
(b) Connect all the static pressure tapping points to the manometer tubes ensuring that one manometer tube remains unconnected to record room air pressure and that one is attached to the first tapping point adjacent to the standard inlet nozzle which should be fitted.
(c) Turn on fan with low airflow (damper plate closed) and read all manometer tubes, including any open to the air (reading should be taken after the fan is on).
(d) Gradually increase air flow by increasing the damper opening to 100%, and take read at all opening.
Measure the diameter of the orifice plate, and the pipe for computing the cross sectional area and Reynolds number.
DATA, OBSERVATION AND RESULTS
Damper Openings (% Openings)
0% 25% 50% 75% 100% Points mm of kerosene Room ‘Pressure’ 96 94 94 94 94 After nozzle 101 103 104 105 104 54 mm 100 104 104 105 104 294 mm 100 104 105 106 105 774 mm 100 106 107 109 107 Before Orifice 100 107 108 110 108 After Orifice 113 180 200 205 208 1574 mm 110 160 176 182 184 2534 mm 107 148 160 164 165
Table 5.1 Static ‘Pressure’ Readings when using Standard Nozzle (80 mm)
Damper Openings (% Openings)
0% 25% 50% 75% 100% Points mm of kerosene Room ‘Pressure’ 95 92 90 90 89 After nozzle 104 130 136 138 140 54 mm 105 132 138 140 141 294 mm 101 116 120 121 122 774 mm 101 118 121 122 123 Before Orifice 102 119 122 124 124 After Orifice 114 178 193 199 202 1574 mm 110 164 177 181 182 2534 mm 108 152 163 167 168
15 Damper Openings (% Opening)
Points 0% 25% 50% 75% 100% Qi 0.039 0.053 0.055 0.058 0.055 Hi 3.279 5.903 6.558 7.214 6.558 Cd 0.599 0.344 0.318 0.330 0.305 Ho 8.526 47.88 60.34 62.30 65.58 Re 26599 36147 37511 39557 37511
Table 2.3: Data of mm (kerosene) for each damper opening (diameter of orifice = 80mm)
Damper Openings (% Opening)
Points 0% 25% 50% 75% 100% Qi 0.020 0.042 0.046 0.047 0.049 Hi 5.903 24.922 30.168 31.480 33.448 Cd 0.820 0.776 0.775 0.771 0.788 Ho 7.87 38.69 46.56 49.19 51.16 Re 34924 73342 80327 82073 85565
Table 2.4: Data of mm (kerosene) for each damper opening (diameter of orifice = 50mm)
Sample Calculation
Taking 0% damper openings with diameter 80mm: A0 = (3.142)(0.082) / 4
= 5.027 x 10-3 m2
ho = (Pk/Pair)(xafter orifice - xbefore orifice)/1000 = (787/1.2)(113-100)/1000 = 8.526 m
h1 = (Pk/Pair)(xafter nozzle - xbefore nozzle)/1000 = (787/1.2)(101-96)/1000 = 3.279 m
C’D = 0.97
Qi = (Ai)(C’d)√2ghi
= (5.027 x 10-3)(0.97) √(2)(9.81)(3.279) = 0.039
Reynold's Number, Re = ud/
= (1.2)(0.039/5.027 x 10-3)0.05 /1.75e-5) = 26599 Cd = Qo Ao 2gho = 0.039 0.005027 (2)(9.81)(8.526) = 0.5998 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 10000 20000 30000 40000 50000 D isch ar ge Coe fficien t, C d Reynolds Number, Re
C
Dagainst Reynold Number for
Standard Nozzle
0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0 20000 40000 60000 80000 100000 D isch ar ge Coe fficien t, C d Reynolds Number, ReC
Dagainst Reynolds Number for
Small Nozzle
17 0 50 100 150 200 250 0 500 1000 1500 2000 2500 3000 Lon git u d ina l Pre ssu re (m m) Tapping Position (mm)
Longitudinal Pressure (mm kerosene) against
Tapping Position for Standard Nozzle
0% 25% 50% 75% 100% 0 50 100 150 200 250 0 500 1000 1500 2000 2500 3000 Lon git u d ina l Pre ssu re (m m) Tapping Position (mm)
Longitudinal Pressure (mm kerosene) against
Tapping Position for Small Nozzle
0% 25% 50% 75% 100%
ANALYSIS AND DISCUSSION
1. Based on the graphs plotted we can witness a sudden change in longitudinal pressure between 1000-1500 mm. This is expected because as the air flows, the orifice plate meter forms a jet that expands to fill up whole pipe, some diameter distance downstream. This will subsequently induce a significant pressure between the two sides of the plate. (Sudden increase in its longitudinal pressure or higher mm of kerosene).
2. CD obtained in the orifice has smaller value in comparison with CD obtained for small nozzle. The two main contributors for the drag coefficient are the skin friction and form drag. These values are calculated by using the same mathematical formula and method. However the CD orifice is acquired by considering the difference of pressure before and after the orifice. Whereas, CD for small nozzle is obtained by taking into consideration the pressure difference between before and after the nozzle.
3. The broader the damper opened, the higher the value of drag coefficient. The relationship between the opening damper and drag coefficient are directly proportional.
4. Based on the graph plotted, as the damper opening increases from 0% to 100% , the longitudinal pressure at each points of the pipe will also generally decrease. The longitudinal pressure achieves maximum value at 208 mm Kerosene for standard nozzle and 202 mm for small nozzle when the damper opening is 100%. The pressure only reaches 113 mm Kerosene and 114 mm Kerosene for standard nozzle and small nozzle respectively when the damper opening is completely closed or at 0%. The data tells us that as the damper opening enlarge, the
manometer readings and also increase. The damper opening provide outlet for air inside the pipe. As the opening become larger, more air can pass through it. Therefore, pressure at the finish of the pipe is reduced.
5. The pressure in the pipe increases after the small opening of the orifice plate where the flow cross-section returns to its original value. The pressure downstream of the matter is lower that the upstream pressure because of the water resistance. The low pressure at the point of highest velocity creates the likelihood for the liquid to partially vaporize. It might remain partially vaporized after the sensor or return to a liquid state as the pressure increases after the lowest point
19 CONCLUSION
In conclusions, since the objectives to determine the discharge coefficient, CD for orifice plate and the small nozzle is effectively done; this experiment can be considered as successful. Based on the data collected and the graph that we plot, we can wrap up that the pressure in the pipe increases after the small opening of the orifice plate where the flow crosses section return to its original value. Yet, because of the meter resistance, the pressure downstream of the meter is lower than the upstream pressure. The low pressure at the point of highest velocity builds the possibility for the liquid to partially vaporize and it might remain partially vaporized after the sensor or it may return to a liquid as the pressure increase after the lowest pressure point.
As the damper opening increases from 0% to 100%, the longitudinal pressure at each points of the pipe will also reduce. In addition, this experiment enlighten the students’ understanding that as the damper opening enlarge from 0% to 50%, its corresponding CD is decreasing, before it rise up as the damper opening increase from 50% to 100%.
