pre-measurement class i. department of fluid mechanics 2009. csaba horváth [email protected]...
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Pre-measurement class I.
Department of Fluid Mechanics
2009.
Csaba Horváth [email protected]
Budapesti University of Technology and Economics
General information
• Department webpage: www.ara.bme.hu
• Student information page: www.ara.bme.hu/poseidon
(materials, test scores, etc.)
• Schedule: 2 pre-measurement classes + 3 measurements (A,B and C) + 2 presentations
1. For the first presentation, the A and half of the B measurement leaders will make presentations
2. For the second presentation, the second half of the B and all of the C measurement leaders will make presentations
• The measurement reports are due within one week of the measurement date, on Friday at noon. The submitting student must send an email to the faculty member checking the report, to notify them that they have submitted the report. The faculty member will correct the report within 3 days and send a message to the student, through the Poseidon network, to let them know if the report has been accepted, corrections need to be made or if the measurement needs to be repeated. If corrections need to be made, the students can consult the faculty member. The corrected reports need to turned in within 2 weeks from the measurement, at noon. An email must once again be sent to the faculty member correcting the report.
Measuring pressure
• U tube manometer
• Betz manometer
• Inclined micro manometer
• Bent tube micro manometer
• EMB-001 digital handheld manometer
Measuring pressure / U tube manometer I.
• Pipe flow
• Butterfly valve
• Average the pressure on pressure taps around the perimeter
H
> g
pB pJ
B Jp p
1 2 ( )ny ny mp gH p g H h g h
The manometers balance equation:
1 2 ( )m nyp p g h
ny <<m
(For example> measuring air with water)
Or
(Measuring water with mercury)
mp g h
( )m nyp g h
Notice that
( )p f H
Measuring pressure / U tube manometer II.
Density of the measuring fluid mf
(approximately)
The manometers balance equation:
Density of the measured fluid: ny (For example air)
31000víz
kgm
3840alkohol
kgm
313600higany
kgm
plevegő = pair -atmospheric pressure [Pa] ~105Pa
R - specific gas constant for air 287[J/kg/K]
T - atmospheric temperature [K] ~293K=20°C
( )m nyp g h
3191
mkg
,RT
p
levegő
levegőlevegő
mercury
water
alcohol
Measuring pressure / U tube manometer III.
Example: the reading:
The exactness ~1mm: The absolute error:
How to write the correct value with the absolute error(!)
The relative error:
10 1h mm mm
10h mm
1h mm
Disadvantages:
• Reading error (take every measurement twice)
• Exactness~1mm
• With a small pressure difference, the relative error is large
Advantages:
• Reliable
• Does not require servicing
%,mmmm
hh
1010101
Measuring pressure / upside down U tube micro manometerThe manometer’s balance
equation
Since the upside down U tube manometer is mostly used for liquid measured fluids, the measurement fluid is usually air. The density of air is13.6 times smaller than mercury and therefore the results are much more exact.
Measuring pressure / Betz micro manometer
The relative error is reduced using optical tools.
10 0,1h mm mm Exactness ~0,1mm: The absolute error is:
The relative error:%,
mmmm
hh
1010101
Measuring pressure / inclined micro manometer
It is characterized by a changing relative error.
The manometers balance equation
1 2 mp p g h
sinh L
Exactness ~1mm,
The relative error:
%,
sinmmmm
sinhL
LL
5050
30101
Measuring pressure / bent tube micro manometer
Is characterized by a constant relative error and not a linearly scaled relative error.
Measuring pressure / EMB-001 digital manometer
List of buttons to be used during the measurementsOn/Off Green buttonReset the calibrations „0” followed by the „STR Nr” (suggested)Changing the channel „CH I/II”Setting 0 Pa „0 Pa”Averaging time(1/3/15s) „Fast/Slow” (F/M/S)
Measurement range:
2p Pa
1250p Pa
Measurement error:
Velocity measurement
• Pitot tube/probe or Static (Prandtl) tube/probe
• Prandtl tube/ probe
Velocity measurement / Pitot tube/probe
Pitot, Henri (1695-1771), French engineer.
2
2d ö stp p p v
Determining the dynamic pressure:
Determining the velocity:
2 2dv p p
Velocity measurement / Prandtl tube/probe
Prandtl, Ludwig von (1875-1953), German fluid mechanics researcher
Measuring volume flow rate
• Definition of volume flow rate
• Measurement method based on velocity measurements in multiple points
• Non-circular cross-sections
• Circular cross-sections
• 10 point method
• 6 point method
• Pipe flow meters based on flow contraction
• Venturi flow meter
• Through flow orifice
• Inlet orifice
• Inlet bell mouth
Measurement method based on velocity measurements in multiple points
Very important: the square root of the averages ≠ the average of the square roots(!)
Example: Measuring the dynamic pressure in multiple points and calculating the velocity from it
2i iv p
1. 2.
3. 4.
1 1
2v p
1 2 3 4 1 2 3 4
1
2 2 2 22
44
n
ii
p p p p p p p pv
vn
Volume flow rate / based on velocity measurements I.Non-circular cross-sections
4
, ,1 1
,1 1 ,2 2 ,3 3 ,4 4
4
n
v v i m i ii iA
m m m m
q vdA q v A
v A v A v A v AAv
1 2 ... . i
AA A áll A
n
Assumptions:
1. 2.
3. 4.
2vq
3vq
1vq
4vq
Volume flow rate / based on velocity measurements II.
Si/D= 0.026, 0.082, 0.146, 0.226, 0.342, 0.658, 0.774, 0.854, 0.918, 0.974
•The velocity profile is assumed to be a 2nd order parabola•Steady flow conditions•Prandtl tube measurements of the dynamic pressure are used
Circular cross-sections, 10 point (6 point) method
Volume flow rate / based on velocity measurements III.
Si/D= 0.026, 0.082, 0.146, 0.226, 0.342, 0.658, 0.774, 0.854, 0.918, 0.974
The advantage of this method as compared to methods based on flow contraction is that the flow is not disturbed as much and is easy to do.
The disadvantage is that the error can be much larger with this method. For long measurements it is also hard to keep the flow conditions constant. (10 points x 1.5 minutes = 15 minutes)
Circular cross-sections, 10 point (6 point) method
1 2 ... .5A
A A áll
1 10 2 9 3 8 4 7 5 6
2 2 2 2 25
v v v v v v v v v v
v
Assumptions:
Volume flow rate / flow contraction methodsVenturi pipe
p1 p2
m
ny
h
H
mq vA .m
kgq áll
s
2 21 1 2 22 2
p v p v
Bernoulli equation (=constant):
Vq vA 3
.V
mq áll
s
1 1 2 2Vq v A v A
A1 A2
1 2A A 1 2v v
A p
1 4 4
1 1
2 2
2 2
1 1
m ny
ny ny
g h pv
d dd d
Volume flow rate / flow contraction methods
Standard orifice size- pressure difference
= d/D Cross-section ratiod [m] Diameter of the smallest cross/sectionD [m] Diameter of the pipe upstream of the orificeReD = Dv/ Reynolds number’s basic equation (characteristic size x velocity)/ kinematic viscosityv [m/s] The average velocity in the pipe of diameter D[m2/s] kinematic viscosityp1 [Pa] The pressure measured upstream of the orificep2 [Pa] The pressure measured in the orifice or downstream of it Expansion number (()~1 For air the change in pressure is small) Contraction ratio, =(,Re) (When using the standard it is 0.6) Heat capacity ratio or Isentropic expansion factor=p2/p1 Pressure ratio
Through flow orifice
2 24v
d pq
Vq vA
Volume flow rate / flow contraction methods
Not a standard contraction – pressure difference
Inlet orifice (not standard)
60
2
4
2
,
pdq mpmpv
beszbesz
v
pdkq
24
2
Determining the uncertainty of the results (error calculation) I.
1. 2.
3. 4.
2p
3p
1p
4p
2 ii
pv
pRT
Example: Pipe volume flow rate uncertainty
41 2 3 4
1 2 3 41
2 2 2 2v i i
i
p RT p RT p RT p RTq v A A A A A
p p p p
1 1 2 2 3 3 4 4
12vq R T A p A p A p A p
p
Pressures measured with the Prandtl tube:p1 =486,2Pap2 =604,8Pap3 =512,4Pap4 =672,0Pa
Ambient conditions:p =1010hPaT=22°C (293K)R=287 J/kg/K
, , ,vq f T p p állandók
Uncertainty of the atmospheric pressure measurements, p=100PaUncertainty of the atmospheric temperature measurements, T=1KUncertainty of the Prandtl pressure measurement with thedigital manometer (EMB-001) p=2Pa
0,1m2
3
0,30822v
mq
Determining the uncertainty of the results (error calculation) I.
1. 2.
3. 4.
2p
3p
1p
4p
Example: Pipe volume flow rate uncertainty
2
1
n
ii i
RR X
X
Typical absolute error
p, T, p)
The absolute error for volume flow rate measurements:
The relative error of volume flow rate measurements:
The results for the volume flow rate:3
50,3082 6,16 *102v
mq
pq
pq
vv 1
21
Tq
Tq
vv 1
21
ii,v
i
v
pq
pq
1
21
0,001976 0,2%v
v
4
1
222
21
21
21
i i
ii,vvvv p
pq
TT
qpp
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