Budapesti University of Technology and
Economics
Department of Fluid
Mechanics
Pre-measurement class I.
Csaba Horváth
2009.
horvath@ara.bme.hu
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:
pB  pJ
H
p 1   ny gH  p 2   ny g ( H  D h )   m g D h
g
>
p 1  p 2  (  m   ny ) g D h
ny <<m
(For example> measuring air
with water)
D
Dp  m g Dh
Or
(Measuring water with mercury)
D p  (  m   ny ) g D h
Notice that D p  f ( H )
p
p
B
J
Measuring pressure / U tube manometer II.
The manometers balance equation:
D p  (  m   ny ) g D h
Density of the measuring fluid mf (approximately)
 h igany  1 3 6 0 0
 víz  1 0 0 0
 alk oh ol
kg
m
kg
3
m
kg
 840 3
m
3
mercury
water
alcohol
Density of the measured fluid: ny (For example air)
levegő 
plevegő
kg
 1,19 3
RTlevegő
m
plevegő = pair -atmospheric pressure [Pa] ~105Pa
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: D h  1 0 m m
The exactness ~1mm: The absolute error:
D  h   1m m
How to write the correct value with the
absolute error(!)
D h  1 0 m m  1m m
The relative error:
D h
Dh

1mm
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:
D h  1 0 m m  0,1m m
The relative error:
D h
Dh

1mm
10 mm
 0 ,01  1 %
Measuring pressure / inclined micro manometer
The manometers balance equation
p1  p 2   m g D h
D h  L sin 
Exactness ~1mm,
The relative error:
L
L

L
Dh
sin 

1mm
 0 ,05  5 %
10 mm
sin 30 
It is characterized by a
changing relative error.
D
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
Green button
Reset 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: D p   1 2 5 0 Pa
Measurement error:  D p  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
Determining the velocity:
v 
2

pd 
2

Dp
v
2
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
vi 
2 D p1
n
v 
vi
i 1
n


2

Dp i

2
v1 
2 Dp2


4
2 Dp3



D p1
2 Dp 4


1.
2.
3.
4.
 D p1  D p 2  D p 3  D p 4 
2

4



Volume flow rate / based on velocity measurements I.
Non-circular cross-sections
4
q v   vdA 
A
q
i 1
n
v ,i

v
m ,i
D Ai 
i 1
v m ,1 A1  v m ,2 A2  v m ,3 A3  v m ,4 A4
 Av
4
Assumptions:
D A1  D A2  ...  áll .  D Ai 
A
n
qv 2
qv 1
1.
2.
qv 3
qv 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 2nd order parabola
•Steady flow conditions
•Prandtl tube measurements of the dynamic pressure are used
Si/D= 0.026, 0.082, 0.146, 0.226, 0.342, 0.658, 0.774, 0.854, 0.918, 0.974
Volume flow rate / based on velocity measurements III.
Circular cross-sections, 10 point (6 point) method
v 1  v 10
v 
2

v2 v9
2
Assumptions:
A1  A2  ...  áll . 

v3 v8
2
5

v4 v7
2

v5 v6
2
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)
Si/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  vA
q m  
qV  vA
qV  
kg
s
3
m
A1
 áll .
A2
 áll .
s
qV  v 1 A1  v 2 A2
H
v1  v 2
A1  A2
p1
ny
Bernoulli equation (=constant):
p1 

2
v1  p2 
2

2
m
2
v2
DA  Dp
v1 
2   m   ny  g D h
 ny
  d 4

1

  1
d2 



2 Dp

 ny
  d 4

1

  1
d2 



p2
Dh
Volume flow rate / flow contraction methods
Through flow orifice
Standard orifice size- pressure difference
qV  vA
d 
2 Dp
4

2
qv   
b = d/D
Cross-section ratio
d [m]
Diameter of the smallest cross/section
D [m]
Diameter of the pipe upstream of the orifice
ReD = Dv/n Reynolds number’s basic equation (characteristic size x velocity)/ kinematic viscosity
v [m/s]
The average velocity in the pipe of diameter D
2
n [m /s]
kinematic viscosity
p1 [Pa]
The pressure measured upstream of the orifice
p2 [Pa]
The pressure measured in the orifice or downstream of it

Expansion number ((b,t,k)~1 For air the change in pressure is small)

Contraction ratio, =(b,Re) (When using the standard it is 0.6)
k
Heat capacity ratio or Isentropic expansion factor
t=p2/p1
Pressure ratio
Volume flow rate / flow contraction methods
Inlet orifice (not standard)
Not a standard contraction – pressure difference
d mp  
2 D p mp
2
qv   
4


  0 ,6
d besz  
2
qv  k 
4

2 D p besz

Determining the uncertainty of the results (error calculation) I.
Example: Pipe volume flow rate uncertainty
Pressures measured with
the Prandtl tube:
p1 =486,2Pa
p2 =604,8Pa
p3 =512,4Pa
p4 =672,0Pa
vi 
2 Dp i
 

4
qv 
v
i
D Ai  A1
i 1
qv 
2R T
1
p
2 D p 1RT
p
 A1 D p 1 
q v  f T , p , D p , állandók
Ambient conditions:
p =1010hPa
T=22°C (293K)
R=287 J/kg/K
Dp2
D p1
1.
Dp3
3.
0,1m2
p
RT
 A2
2 D p 2 RT
p
 A3
2 D p 3 RT
A2 D p 2  A3 D p 3  A 4 D p 4 
p
 A4
2 D p 4 RT
p
q v  0, 3 0 8 2
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) Dp=2Pa
2
.
4.
Dp 4
Determining the uncertainty of the results (error calculation) I.
Example: Pipe volume flow rate uncertainty

R 

X
  i X 
i 1 
i 
n
R 
Dp2
D p1
Typical absolute error
2
qv
 1 1
 qv    
p
 2 p
1.
Dp3
qv
 1 1
 qv   
T
2 T
qv
 1 1
 qv ,i    
Dpi 
 2  Dpi
p, T, Dp)
2
.
3.
4.
The absolute error for volume flow rate measurements:
2
qv 
2


p  1 
T  1 
q




q

   


 v

 v
p
2
T


 2 



 D p i   1  
q

  
  v ,i
D
p
i 1 
 2 
i
4
The relative error of volume flow rate measurements:
 qv
 0, 0 0 1 9 7 6  0, 2 %
qv
The results for the volume flow rate:
q v  0, 3 0 8 2  6,1 6 * 1 0
5
m
2
3
2
Dp 4
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