Transcript Measuring pressure / U tube manometer I.
2009.
Budapesti University of Technology and Economics
Department of Fluid Mechanics
Pre-measurement class I.
Csaba Horváth
• • • •
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 The manometers balance equation:
p B p
1
ny gH
p J
p
2
ny p
1
p
2 (
m
ny
)
h
m
H ny << m (For example> measuring air with water)
m
Or (Measuring water with mercury) (
m
ny
) Notice that ) p B > D J p g
Measuring pressure / U tube manometer II.
The manometers balance equation: (
m
ny
) Density of the measuring fluid mf (approximately)
higany
13600
kg m
3 mercury
víz
1000
kg m
3 water
alkohol
840
kg m
3 alcohol Density of the measured fluid: ny (For example air)
leveg ő
p leveg ő RT leveg ő
1
,
19
kg m
3
p levegő = p air -atmospheric pressure [Pa] ~10 5 Pa R - specific gas constant for air 287[J/kg/K] T - atmospheric temperature [K] ~293K=20 °C
D
Measuring pressure / U tube manometer III.
Example: the reading: 10
mm
The exactness ~1mm: The absolute error: D
h
1
mm
How to write the correct value with the absolute error(!) 10
mm
1
mm
The relative error: D
h
D
h
1
mm
10
mm
0
,
1 10
%
• • • 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
Measuring pressure / upside down U tube micro manometer
The 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.
Exactness ~0,1mm: The absolute error is: 10
mm
0,1
mm
D
h
D
h
1
mm
10
mm
0
,
01 1
%
Measuring pressure / inclined micro manometer
The manometers balance equation
p
1
p
2
m L
sin D Exactness ~1mm, The relative error:
L
L
D
L h sin
1
mm
10
mm sin
30 0
,
05 5
%
It is characterized by a changing relative error.
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 measurements On/Off Reset the calibrations Changing the channel Setting 0 Pa Averaging time(1/3/15s) Green button „0” followed by the „STR Nr” (suggested) „CH I/II” „0 Pa” „Fast/Slow” (F/M/S) Measurement range:
p
1250
Pa
Measurement error: D 2
Pa
Velocity measurement
• • Pitot tube/probe or Static (Prandtl) tube/probe Prandtl tube/ probe
Velocity measurement / Pitot tube/probe
Pitot, Henri (1695-1771), French engineer.
Determining the dynamic pressure:
p d
p ö
p st
2
v
2 Determining the velocity:
v
2
p d
2 D
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
v i
2 D
p i v
1 2 D
p
1 1.
2.
3.
4.
v
i n
1
v i n
2 D
p
1 2 D
p
2 4 2 D
p
3 2 D
p
4 2
p
1
p
2 D
p
3 4 D
p
4
Volume flow rate / based on velocity measurements I.
Non-circular cross-sections
q v
v m
,1
A
1
A
vdA
v m
,2
A
2
i
4 1
q
v m
,3
A
3
i n
1
v
D
A i
v m
,4
A
4 4 Assumptions:
Av
D D
A
2 ...
áll
.
D
A i
A n q v
1
q v
2 1.
2.
q v
3
q v
4 3.
4.
Volume flow rate / based on velocity measurements II.
Circular cross-sections, 10 point (6 point) method
•The velocity profile is assumed to be a 2 nd order parabola •Steady flow conditions •Prandtl tube measurements of the dynamic pressure are used S i /D= 0.026, 0.082, 0.146, 0.226, 0.342, 0.658, 0.774, 0.854, 0.918, 0.974
v
Volume flow rate / based on velocity measurements III.
Circular cross-sections, 10 point (6 point) method
v
1
v
10 2
v
2
v
9 2
v
3 2 5
v
8
v
4
v
7 2
v
5
v
6 2 Assumptions:
A
1
A
2 ...
áll
.
A
5 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) S i /D= 0.026, 0.082, 0.146, 0.226, 0.342, 0.658, 0.774, 0.854, 0.918, 0.974
Volume flow rate / flow contraction methods Venturi pipe
q m q V
vA
vA
kg s m
3
s
áll
.
áll
.
A 1
q V
v A
1 1
v A
2 2
A
1
A
2
v
Bernoulli equation ( =constant):
p
1 2
v
1 2
p
2 2
v
2 2
p
1
v
2
v
1 2
m
ny
ny
d d
2 1 4 1
ny
2 D
p
d d
2 1 4 1 ny p 1 m A 2 p 2 H D h
Volume flow rate / flow contraction methods Through flow orifice
Standard orifice size- pressure difference
q V
vA q v
d
2 4 2 D
p
b = d/D d [m] Cross-section ratio Diameter of the smallest cross/section D [m] Re D = Dv/ n v [m/s] n [m 2 /s] p 1 [Pa] p 2 k [Pa] t =p 2 /p 1 Diameter of the pipe upstream of the orifice Reynolds number’s basic equation (characteristic size x velocity)/ kinematic viscosity The average velocity in the pipe of diameter D kinematic viscosity The pressure measured upstream of the orifice The pressure measured in the orifice or downstream of it Expansion number ( Contraction ratio, Pressure ratio =( b ( b,t,k )~1 For air the change in pressure is small) ,Re) (When using the standard it is 0.6) Heat capacity ratio or Isentropic expansion factor
Volume flow rate / flow contraction methods Inlet orifice (not standard)
Not a standard contraction – pressure difference
q v
d
2
mp
4 0
,
6 2 D
p mp
q v
k
d
2
besz
4 2 D
p besz
Determining the uncertainty of the results (error calculation) I.
Example: Pipe volume flow rate uncertainty
D
p
1 Pressures measured with the Prandtl tube: p 1 p 2 p 3 p 4 =486,2Pa =604,8Pa =512,4Pa
v i
=672,0Pa 2 D
p i
p RT
Ambient conditions: p =1010hPa T=22 °C (293K) R=287 J/kg/K D
p
3 1.
3.
0,1m 2 .
2 4.
D
p
2 D
p
4
q v q v q v
i
4
1
v i
D
A i
A
1 2 D
p
A
2 2 D
p
A
3 2
R T
1 1 D D D D
p
D
p állandók
4 2 D
p
A
4 2 D
p q v
0,3082
m
3 2 Uncertainty of the atmospheric pressure measurements, p=100Pa Uncertainty of the atmospheric temperature measurements, T=1K Uncertainty of the Prandtl pressure measurement with the digital manometer (EMB-001) D p=2Pa
Determining the uncertainty of the results (error calculation) I.
Example: Pipe volume flow rate uncertainty
Typical absolute error D
p
1
R
i n
1
X i
R
X i
2 p, T, D p)
q v
p
q v
1 2 1
p
q v
T
q v
i q v
1 2
q v , i
1
T
1 2 1 D
p i
D
p
3 1.
3.
.
2 4.
D
p
2 D
p
4 The absolute error for volume flow rate measurements:
q v
q v
p p
1 2 2
q v
T T
1 2 2
i
4 1
q v , i
D
p p i i
1 2 2 The relative error of volume flow rate measurements:
q v q v
0,001976 0,2% The results for the volume flow rate:
q v
0,3082 6,16 * 10 5
m
3 2
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