Pre-measurement class I.

Department of Fluid Mechanics

2009.

Csaba Horváth horvath@ara.bme.hu

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

qq

4

1

222

21

21

21

i i

ii,vvvv p

pq

TT

qpp

qq

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