HB015(E) Teori Bernoulli

7/25/2019 HB015(E) Teori Bernoulli

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A 010312

INSTRUCTION MANUAL

HB 015 BERNOULLISTHEOREM APPARATUS

ESSOM COMPANY LIMITED508 SOI 22/1 SOMDET PHRACHAO TAKSIN RD.BUKKALO THONBURI BANGKOK 10600, THAILANDTEL. +66 (0) 24760034 FAX +66 (0) 24761500

E-mail: [email protected]
mailto:[email protected]:[email protected]


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1 300414

CONTENTS

Page

Receipt of goods A

Installation instructions B

1. General description 1-12. Theory 2-1

3.

Test procedures 3-14. Typical data 4-1

5. Sample calculations 5-16. Observations 6-1

Addendum

Addendum 1 Water manometer

Addendum 2 Venturi tube dimensions at different pressure taps and diameter

All rights reserved. No part of this publication may be reproduced in any material form (including photocopying

or storing in any medium by electronic means and whether or not transiently or incidentally to some other use of this

publication) without the written permission from ESSOM COMPANY LIMITED.


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A 110711

RECEIPT OF GOODS

1. On Receipt of Goods

a) On receipt of the goods at the consignees premises, the shipment should be immediately inspected for any damagesor missing package. This should be checked against the packing list or shipping documents. Any damage should be

reported immediately to the insurance agent.

b) The package should then be open to check items or parts against the delivery list. Any damaged or missing items

should be immediately claimed to the insurance agent with copy to the supplier.c) If insurance has been arranged by the buyer then you must notify your insurer in writing of any damage or loss of

parts which was observed regarding this shipment within a specified period of time as stated in the Terms and

Conditions. This should include detailed photographs of the damaged equipment.

d) If insurance has been arranged by the seller you should notify the insurances representative along with anycorrespondence including the insurance certificate supplied by the seller. These should include detailed photographs for

evaluation of damages or replacement parts pertaining to the shipment.

e) The supplier will only replace damaged items or missing on notification by the insurance company that the claim has

been accepted. The insurance company may refuse responsibility if parts are damaged or missing while under custodys

for a long time without prior claim. Immediate claim is therefore vital.

2. Manufacturers Liability

a) Before proceeding to install, commission, or operate the equipment listed in the instruction manual, we would like to

alert the user to the health and safety aspects of people who will work on or operate our equipment with regard to theliability of the manufacturers or suppliers.

b) Manufacturers or suppliers are absolved of any responsibilities with regard to misuse of their equipment causing

harm or financial charges being incurred against them from clients or third parties for consequences of failure or

damage of the equipment in any way if the equipment is not installed, maintained and operated as outlined in theinstruction manual published by the manufacturers or suppliers.

c) In order to safeguard the students and operators of the equipment it is vital that all safety aspects as outlined in the

instruction manual are observed.


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010312B

INSTALLATION INSTRUCTIONS

1. GENERAL INSTRUCTION

Shipped oversea Equipment is usually partially assembled in order to reduce possibility of damages and

shipping volume.

Parts list or packaging list is normally shipped with shipping documents. When the shipping box reach the site,

the box should be carefully opened, and the parts must be checked / examined for damage and identified accordingto the part list.

Equipment and parts are to be assembled according to the assembly instruction.

2. ASSEMBLY INSTRUCTIONS FOR MODEL HB 015 BERNOULLIS THEOREM APPARATUS

2.1 Connect the male coupling hose to water inlet of the apparatus, the other end of hose is ready to be connected

to Hydraulic Bench water outlet.

2.2 Screw the hand air pump onto the manometer top chamber.


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1-1 301013

INSTRUCTION MANUAL

HB 015 BERNOULLIS THEOREM APPARATUS

1. GENERAL DESCRIPTION

Bernoullis theorem is applied on flow through a clear acrylic Venturi tube. The apparatus is to be used withHB 100 Hydraulics Bench (separately supplied).

Static pressures at various points along the wall of a transparent Venturi tube are directly measured on a

manometer equipped with a vent valve and a hand air pump. A movable stainless steel total head probe is also

provided. Flow through the Venturi tube is controlled by a valve at the outlet. As a primary flow measuring device,coefficient of discharge for the Venturi tube can also be determined.

Outlet

Flow control valve

Total head probe

Pressurizing valve

for hand air pump

Inlet

Venturi tube

Watermanometer

Air reliefvalve

Figure 1-1HB 015 Bernoullis theorem apparatus

1.1 Main Components Are

1.1.1 The Venturi tube consists a 28 mm inside diameter pipe and a 14 mm inside diameter throat of 21inlet

angle and a 10ooutlet angle. Seven pressure tapping points along the wall of the tube for connecting to

the manometer.

1.1.2 The water manometer consists of 8 tubes or more 450 mm long along with a white acrylic back platefor easy viewing, a top air chamber and a bleed valve to vary the chamber pressure by means of a hand

air pump.

1.1.3 A total head probe of stainless steel tube (1.9 mm inside diameter) which can be moved axially along

the Venturi tube. The total head tube is connected to manometer tube No. 7 or next to the last by a hose

pipe.

1.1.4 A rotameter (optional) with a flow rate up to 35 lpm. The outlet control valve of the Venturi tube is used

for controlling the flow of water as well as to raise or lower the pressure in the system.

1.1.5 All the equipment is mounted on a steel frame with adjusting screws to maintain a level condition.

1.2 Technical Data1.2.1 Diameter : 28 mm inlet with 14 mm throat

1.2.2 Taper angles : Inlet 21o, outlet 10o1.2.3 Water manometer : 8 tubes x 450 mm x 1 mm graduation

1.2.4 Total head probe : 3 mm tube


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2. THEORY

Bernoullis Theorem states that The total head of the liquid flowing between two points remains constant

provided there is no loss due to friction and no gain due to an application of outside work between these twopoints

The total head (H) of a flowing liquid is made up of an elevation head or static Head (Z), pressure head (p/) andvelocity head (V

2/2g), mutually convertible into each othersform.

H = Z2g

Vp 2

Where : H = total head , m

V = velocity , m/s

p = pressure , N/m

Z = elevation , m

g = acceleration due to gravity = 9.81 m/s

= specific weight of fluid , N/m3

Thus for point 1 and 2

1

21 Z

2g

V1p

= 2f,12

22 hZ

2g

V2p

(2-1)

Where: hf, 1-2 = Friction loss between 1 and 2.

Flow

Total head probe to

Manometer tube No.7

or next to the last

(1) (2) (3) (4) (5) (6) (7) (8)

D1 = 28 mm D2 = 21 mm D3 = 14 mm D4 = 16.8 mm

D5 = 19.6 mm D6 = 22.4 mm D7 = 25.2 mm D8 = 28 mm

Pressure tap

Note:For pressure tap more than 8 taps and other diameters of pipe and throat see Addendum 2

Figure 2-1Bernoullis tube with differences in diameters

If the Bernoullis tube is in a horizontal position then Z1= Z2and if the friction loss between point 1 and 2 is

very small, Then:

2g

V1p

2

1

=2g

V2p 2

2

(2-2)

or

2p1p =

2g

V

2g

V 2122 (2-3)

Since section (1) and section (2) of the Bernoullis tube are different in diameter then velocity V1is different

from V2. This can be demonstrated by the water levels at point 1 and 2 of the manometer. From the Bernoullis theorem

we can see that the lowest pressure will be at the throat of the tube.

We can further calculate the difference of pressure head between two points and can compare it with a

measured value. The difference between the theoretical and measured value is mainly due to frictional losses.

If: Vol = Volume of flow measured from the measuring tank, m3

t = Measuring time, s

A = Cross-section area, m2

D = Diameter of Bernoullis tube section, m


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From equation (2-3) we have

2p1p =g2

VV 2122 m.

g2

VV 2122 =

2

1

2

2 A

Vol/t

A

Vol/t

2g

1

=

2

21

2

22

2

2

D

4

D

4

t2g

Vol

=

41

42

22

2

D

1

D

1

tg

Vol8 m. ...(2-4)

2p =

4142

22

2

D

1

D

1

gt

Vol81

p m. (2-5)

The dimension of equation (2-4) and (2-5) are in m.

Since the diameter of the tube at each particular section along the tubes length is fixed. Then we can calculate

the pressure drop along the tube if the flow rate is known. The difference between the theoretical pressure drop andthe actual pressure drop (measured value) is due to the friction in the tube between these two points.

At the same time we can compare the total head at any point along the Venturi tube using a total head probe

(Pitot tubes probe) whose total head is shownon tube No.7 or next to the last.

s

2s Z

2g

Vsp

= Z

2g

Vp 2

m. (2-6)

At the stagnation point in front of the Pitot tube tip Vs= 0 and Zs= Z:

sp

= 2g

Vp 2

m. (2-7)

Or2g

V2 =

psp m.

Velocity head =

psp m. (2-8)

Therefore the velocity head can be demonstrated by the difference of total head or stagnation pressure head

(ps/) measured from Pitot tube and static pressure head (p/) at that point.


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3. TEST PROCEDURES

Outlet

Flow control valve

Total head probe

Pressurizing valve

for hand air pump

Inlet

Venturi tube

Watermanometer

Air reliefvalve

Figure 3-1Bernoullis theorem apparatus

3.1 Apparatus Operation

3.1.1 If the apparatus outlet control valve is slightly closed, the system pressure will increase. Hench water

level in the manometer will be higher and vise versa.

3.1.2 A hand air pump is used to increase air pressure in the manometer via the pressurizing valve.

If air is pumped into the manometer top chamber, air pressure in the manometer will increase and thewater level will be lower and vise versa.

3.2 BernoullisTheorem Test

3.2.1 Place the apparatus on top of the bench and connect the Hydraulic Benchs water outlet to the test

apparatus with the apparatus outlet control valve open and the apparatus discharges to the benchmeasuring tank.

3.2.2 Start the pump and slowly open the bench flow control valve to obtain a small flow such as 5 lpm.

Adjust the apparatus outlet control valve and / or top air chamber (by means of a hand air pump) such

that the water levels in all tubes of the manometer can be observed. (See 3-1)3.2.3 Adjust the flow rate to about 5 lpm and record:

3.2.3.1 Flow volume by the bench measuring tank.

3.2.3.2 Time for the flow by stop watch.

3.2.4 Move the total head probe to be in line (vertical plane) with the manometer tapping point no. 1.

3.2.5 Record:

- Manometer readings for tube no.1 and no. 7 (total head) or next to the last.

3.2.6

Repeat step 3.2.4 and 3.2.5 for tappingpoint no 2, 3 to the last tapping point.3.2.7 Repeat step 3.2.3 to 3.2.6 for other flow rate such as 10, 15 20 lpm.


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DATA SHEET


Tested by: . Date: ...

Dia. throat x dia. pipe: ...................mm

Volume: l, time ...s, flow rate ... lps = ...lpm

Pointno.

Measured

static head(p/)act

cm

Theoretical

diff. vel. head

g2

VV 212n , cm

Theoretical

static head(p/)th

cm

Difference

100

p/

p/

th

%

Actual total head (Tube No.7

or next to the last) Hact

cm

Head loss

Hactcm

1

2

3

4

5

6

7

8

910

11

Volume: l, time ...s, flow rate ... lps = ...lpm

Point

no.

Measured

static head

(p/)actcm

Theoretical

diff. vel. head

g2

VV 212n , cm

Theoretical

static head

(p/)thcm

Difference

100

p/

p/

th

%



cm

Head loss

Hactcm

1

2

3

4

56

7

8

9

10

11

Volume: l, time ..s, flow rate ... lps= .....lpm

Point

no.

Measured

static head

(p/)actcm

Theoretical

diff. vel. head

g2

VV 212n , cm

Theoretical

static head

(p/)thcm

Difference

100

p/

p/

th

%



cm

Head loss

Hactcm

1

2

3

4

5

6

7

8

9

10

11

Note: 1. p/ =p/thp/act 2. Hact= H1act- Hnact 3. Point no.7 or next to the last point will be blinded.


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4. TYPICAL DATA

DATA SHEET


Tested by: K. Pornsit Date: ..09/11/02...

Dia. throat x dia. pipe: 14 x 28...mm

Volume: 10l, time 30.83.s, flowrate 0.3243. lps = 19.46..lpm

Point

no.

Measuredstatic head

(p/)actcm

Theoretical diff.vel. head

g2

VV 212n , cm

Theoreticalstatic head

(p/)thcm

Difference

100

p/

p/

th

%



cm

Head loss

Hactcm

1 42.40 0.00 42.40 0.00 42.40 0

2 38.40 3.06 39.34 2.39 42.10 0.30

3 19.20 21.23 21.17 9.31 42.00 0.40

4 29.00 9.51 32.89 11.84 41.90 0.50

5 33.50 4.48 37.92 11.66 41.50 0.90

6 36.50 2.04 40.36 9.56 41.40 1.00

7 - - - - - -

8 38.00 0.00 42.40 10.38 41.20 1.20

910

11

Volume: 10l, time 96.93.s, flow rate 0.1031. lps = 6.19...lpm

Point

no.

Measured

static head

(p/)actcm

Theoretical diff.

vel. head

g2

VV 212n , cm

Theoretical

static head

(p/)thcm

Difference

100

p/

p/

th

%



cm

Head loss

Hactcm

1 14.10 0.00 14.10 0.00 14.10 0

2 13.70 0.31 13.79 0.66 13.60 0.50

3 11.50 2.15 11.95 3.78 13.50 0.60

4 12.00 0.96 13.14 8.66 13.40 0.70

5 12.40

0.45 13.65

9.14

13.40

0.70

6 13.00 0.21 13.89 6.43 13.30 0.80

7 - - - - - -

8 13.20 0.00 14.10 6.38 13.20 0.90

9

10

11

Volume: 10l, time 141.84.s, flow rate 0.0705. lps= 4.23...lpm

Point

no.

Measured

static head

(p/)actcm

Theoretical diff.

vel. head

g2

VV 212n , cm

Theoretical

static head

(p/)thcm

Difference

100

p/

p/

th

%



cm

Head loss

Hactcm

1 10.00 0.00 10.00 0.00 11.00 0

2 9.80 0.14 9.86 0.56 10.80 0.20

3 8.60 1.00 9.00 4.41 10.60 0.40

4 8.90 0.45 9.55 6.81 10.60 0.40

5 9.40 0.21 9.79 3.97 10.50 0.50

6 9.60 0.10 9.90 3.07 10.40 0.60

7 - - - - - -

8 9.70 0.00 10.00 3.00 10.30 0.70

9

10

11

Note: 1. p/ =p/thp/act 2. Hact= H1act- Hnact 3. Point no.7 or next to the last point will be blinded.


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5. SAMPLE CALCULATIONS

Test runs were conducted by a team of engineers and technicians at ESSOM factory prior to shipment to

customer. Typical test data were shown below.

Flow rate, Q = 0.3243 lps

Diameters of pipe, D1 = 28 mm

Diameters of pipe, D2 = 21 mm

From Vol., t and (p1/) for each flow rate we can calculate (p2/), (p3/), (p4/), (p5/), (p6/), (p7/), and (p8/)

by using equation (2-4). Comparison of (p2/), (p3/), (p4/), (p5/), (p6/), (p7/), and (p8/) with the measuredvalues can then be made.

Flow of volume from measuring tank is 10 l

Measuring time, t = 30.83 s

Q =time

Vol=

l1,000

ml

s30.83

l10 3 = 3.24 10-4

s

m3

From equation (2-4),g2

VV 2122 =

41

42

22

2

D

1

D

1

tg

Vol8

=

4142

2

2

D

1

D

1

g

Q8

=

41

42

2

2

2

624

D

1

D

1

s

m9.81

s

m103.24

8

=

41

42

59

D

1

D

1m108.6993

=

44

59

m)(0.028

1

m)(0.021

1m108.6993

=

4

59

m

1

1873,514,964.m108.6993

= 0.0306 m = 3.06 cm

From equation (2-5), the theoretical static head of measuring point number 2 is:

2p =

4142

22

2

D

1

D

1

gt

Vol81

p

= 0.4240 m0.0306 m = 0.3934 m

= 39.34 cmBecause the measured (actual) pressure head is equal to 38.40 cm and the calculated (theoretical)

pressure head is 39.34 cm then the percentage of pressure head difference will be:

p% = 100%

2p

2p2p

th

actth

= 100%cm39.34

mc38.4mc39.34

= 2.39 %

Head loss between point (1) and point (2)

2L,1h = 21 HH

= 42.40 cm - 42.10 cm

= 0.30 cm


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6. OBSERVATIONS

When carrying out the actual tests there is a small frictional loss and the following observation can be made.

6.1 At any flow rate the manometer recording at tube no. 8 (the last tube) is lower than tube no. 1 despite Venturi

tubes diameter being the same. This difference represents friction loss between Point 1 and 8 (the last).

6.2 As the Pitot tube probe is slowly moved from point no. 1 to point no. 8 (the last), the Pitot probe reading at tube

no. 7 (or next to the last) slowly decreases, this show that the frictional loss increases as the Pitot tube probe

moves along the length of the Venturi tube.


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010312

ADDENDUM 1

WATER MANOMETER


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010312

WATER MANOMETER

Description

This manometer employs clear acrylic tubes

with a top common chamber. This chamber has

an air relief valve and can be pressurized by a

hand air pump or may be reduced by opening a

vent valve. Pressure ports are at the bottom.

Range : 0-450 or 950 mm

Graduation : 1 mm

Application : Comparison of water pressures

This manometer uses 2 clear acrylic tubes.

For multiple reading, the number of tubes may

be 4, 6, 8, 10 or more are available as an option.

Instruction for Use

1. Close the vent valve at the top chamber.

2. Connect pressure lines from the pressure

source to the inlet pressure ports of themanometer. Water levels will show on themanometer scale.

3. If the levels are too low, release pressure from

the top chamber by opening the vent valve or

increase static pressure of the system to be

measured by closing the system outlet valve. If

the levels are too high, open the outlet valve of

the system slightly more or increase the top

chamber pressure by hand air pump via air

pressuring valve.

4. If differential pressure exceeds the water

manometer range. Close the water manometer

inlet valves and use the mercury manometeronly.

Note:More than one pair of tubes may be used simultaneously if average pressure from one pair is not much differentfrom the other pairs. In this case, down stream average pressure is always lower than up stream average pressure. Thus,

if anyone pair of water levels are out of the manometer range, that pair can not be used, simply close the inlet valves of

that pair by or close the pressure tapping ports at the pressure source.

Multi-Tube ManometerTwo-Tube Manometer

Pressure inlet valve

Pressurizing valve for

hand air pump

Top chamber

Pressure line

Air bleeding valve


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010312

ADDENDUM 2

VENTURI TUBE DIMENSIONS AT DIFFERENT PRESSURE TAPS AND

DIAMETERS


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010312

VENTURI TUBE DIMENSIONS AT DIFFERENT PRESSURE TAPS AND DIAMETERS

Flow

(6) (7) (8) (9)

Pressure tap

D1 = 28 mm D2 = 28 mm D3 = 24.29 mm D4 = 18.73 mm D5 = 14 mm D6 = 15.76 mm

D7 = 18.38 mm D8 = 21 mm D9 = 23.63 mm D10 = 26.26 mm D11 = 28 mm

(11)(10)(5)(4)(3)(2)(1)

Total head probe to

Manometer tube No.10

For 14 mm throat x 28 mm pipe diameter

D1 = 26 mm D2 = 26 mm D3 = 24.15 mm D4 = 18.59 mm D5 = 16 mm D6 = 16.66 mmD7 = 18.85 mm D8 = 21.04 mm D9 = 23.22 mm D10 = 25.41 mm D11 = 26 mm

For 16 mm throat x 26 mm pipe diameter

Figure A2-1 Venturi tube with 11 pressure taps

HB015(E) Teori Bernoulli

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