Calc. Referefces

8/12/2019 Calc. Referefces

1/21

Results

Head loss through smooth and rough pipes and the relationship between the

friction factor ( f) and Re number:

The determination of the experimental head loss for the smooth and rough pipes was

determined through the following equation:

[1]

Where; is converted from (cm H2O) to (!m2)" which is equivalent to (#a) using $quation

2" is the densit% of the water" which equal to &&'*'& +g!m," and is the gravit% in (m!s2)

The theoretical head loss was calculated using the pipe friction equation -elow (h theo)

Where; f is the friction .actor" / is the length of the pipe (all pipes are 0 m long)"

and 1 is the inner diameter of pipe (m)

The velocit% of the flow rate (m!s) was calculated using $quation *

[2]

Where; is the volumetric flow rate of the water in (m,!s)

Then 3e%nolds num-er needed to -e calculated using $quation 4 in order to find the

friction factor (f) for all pipes (except the first pipe (d = 17mm)) from mood% chart

5lso the relative roughness needed to -e calculated using $quation 6

[2]


2/21


3/21

Ta-le 0 shows" the pressure drop for each flow rate in (#a)" the experimental head loss" and

the percentage error -etween the theoretical and experimental head loss The friction factor

for this pipe is calculated using the following correlation" not from mood% chart -ecause thevalue of relative roughness is outside the range of mood% chart

[2]

Figure 1: The relation between the head loss (h) and the flow rate (#) for rough pipe (D = 17

mm)!

.igure 0 are o-tained -% plotting the experimental and theoretical head loss in (m) versus the

water flow rate in (m,!s)" while figure 2 represent the relation -etween the friction factor and

3e%nolds9s num-er" which is as 3e%nolds9s num-er increase" the friction factor decrease

3


4/21

Figure ": Relation betweenf andRe for rough pipe (D = 17 mm)!

Table ": Data needed to calculate hexpfor rough pipe (D = "& mm) with rough () = 1!1" mm!

#

$%min#

(m&%s)

D

(m)u (m%s) Re

'

(cm

"o)

'

(a)

hexp(m)

%D fhtheo(m)

*

error

00.000

33

2

,

0.80229

403

19164.8

8365

490.33

25

0.0501

31

0.0486

96

0.017

24

0.0983

64

49.035

46

5

0.000

422,

1.00286

753

23956.1

0449.7

951.24

51

0.0972

54

0.0486

96

0.017

19

0.1532

48

36.538

37

00.000

50

2

,

1.20344

104

28747.3

25314.5

1421.9

64

0.1453

8

0.0486

96

0.017

16

0.2202

93

34.006

13

50.000

58

2

,

1.40401

455

33538.5

46220.5

2010.3

63

0.2055

37

0.0486

96

0.017

14

0.2994

93

31.371

85

00.000

67

2

,

1.60458

805

38329.7

67127

2647.7

96

0.2707

07

0.0486

96

0.017

12

0.3907

19

30.715

61

4


5/21

Figure &: The relation between the head loss (h) and the flow rate (#) for rough pipe (D = "& mm)!

Figure +: Relation betweenf andRe for rough pipe (D = "& mm)!

For ,mooth ipes:

.or smooth pipes the roughness of the pipe (8) equal ero

Table &: Data needed to calculate hexpfor ,mooth pipe (D = -!. mm)!

#

($%min

)

#

(m&%s

)

D

(m) u (m%s) Re

'

(cm

"o)

'

(a)

hexp(m)

f

htheo(

m)

*

error

70.000

12

64

3.51585

181

23734.9

712171.5

16818

.4

1.719

49

0.00636

4729

2.467

679

30.31

953

5


6/21

90.000

15

64

4.52038

09

30516.3

915238.6

23398

.67

2.392

247

0.00597

7145

3.830

818

37.55

257

110.000

18

64

5.52490

999

37297.8

118350

34323

.28

3.509

164

0.00568

4683

5.442

573

35.52

381

130.000

22

64

6.52943

908

44079.2

322450.1

44139

.73

4.512

785

0.00545

216

7.290

679

38.10

199

170.000

28

64

8.53849

726

57642.0

728737

72275

.01

7.389

297

0.00509

8497

11.65

877

36.62

026

Figure .: The relation between the head loss (h) and the flow rate (#) for,mooth pipe (D = -!. mm)!

Figure -: Relation betweenf andRe for smooth pipe (D = -!. mm)!

6


7/21

Table +: Data needed to calculate hexpfor ,mooth pipe (D = 1-!. mm)!

#

($%m

in)

#

(m&%s

)

D

(m)u (m%s) Re

'

(cm

"o)

'

(a)

hexp(m)

fhtheo(m)

*

error

20 0.000

33

0

64

1.55891

107

26714.6

86216.6 1627.

904

0.166

435

0.006179

304

0.185

549

10.301

65

250.000

42

0

64

1.94863

884

33393.3

57727.7

2716.

442

0.277

725

0.005844

025

0.274

19

1.2893

05

300.000

50

0

64

2.33836

661

40072.0

29238.2

3746.

140.383

0.005583

632

0.377

241

1.5266

38

350.000

58

0

64

2.72809

438

46750.7

00852

5099.

458

0.521

362

0.005372

545

0.494

056

5.5268

81

400.000

67

0

64

3.11782

215

53429.3

72367

6570.

456

0.671

754

0.005196

155

0.624

111

7.6337

95

Figure 7: The relation between the head loss (h) and the flow rate (#) for,mooth pipe (D = 1-!. mm)!

7


8/21

Figure /: Relation betweenf andRe for smooth pipe (D = 1-!. mm)!

Table .: Data needed to calculate hexpfor ,mooth pipe (D = "-!- mm)!

#

($%mi

n)

#

(m&%s

)

D

(m)

u

(m%s)Re

'

(cm

"o)

'

(a)

hexp(m)

fhtheo(m)

*

error

200.000

33

2

66

0.59982

693

16571.1

3990.2

19.61

33

0.002

005

0.006962

881

0.019

201

89.556

52

250.000

42

2

66

0.74978

366

20713.9

2491.2

117.6

798

0.012

031

0.006585

087

0.028

373

57.596

27

300.000

50

2

66

0.89974

039

24856.7

0992.2

215.7

463

0.022

058

0.006291

674

0.039

037

43.496

11

35

0.000

58 266

1.04969

712

28999.4

9493.7

362.8

461

0.037

097

0.006053

82

0.051

125

27.439

46

400.000

67

2

66

1.19965

385

33142.2

7985

490.3

325

0.050

131

0.005855

062

0.064

584

22.378

35

8


9/21

Figure 0: The relation between the head loss (h) and the flow rate (#) for,mooth pipe (D = "-!- mm)!

Figure 1: Relation betweenf andRe for smooth pipe (D = "-!- mm)!

Determine the head loss for the fittings:

The experimental resistance coefficient () for a fitting can -e calculated from

following correlation


10/21

Kexp = (>)

For the 2al3es:

Table -: Data needed to calculate hexpand4expfor gate 3al3e (D = "& mm)!

#

$%mi

)

#

(m&%

s)

D

(m)

u

(m%s)Re

'

(cm

"o)

'

(a)

hexp(m)

4exp4th

5.6

htheo(m)

h *

error

4 *

error

00.00

033

2,

0.802

7

1917

4.59

0.219.61

33

0.0020

05237

0.061

06

0

,

0.004

2692

53.03

066

53.03

066

50.00

042

2,

1.003

375

2396

8.241.2

117.6

798

0.0120

3142

0.234

471

0

,

0.006

6707

-

80.36

23

-

80.36

23

00.00

050

2,

1.204

05

2876

1.882.7

264.7

796

0.0270

70695

0.366

361

0

,

0.009

6058

-

181.8

16

-

181.8

16

50.00

058

2,

1.404

725

3355

5.534

392.2

66

0.0401

04734

0.398

76

0

,

0.013

0746

-

206.7

39

-

206.7

39

00.00

067

2,

1.605

401

3834

9.186.1

598.2

057

0.0611

59719

0.465

584

0

,

0.017

077

-

258.1

41

-

258.1

41

The average experimental fitting constant equals to 0.305247

10


11/21

Figure 11: The relation between the head loss (h) and the flow rate (#) forgate 3al3e (D = "& mm)!

.igure 00 illustrate that the difference -etween the theoretical and experimental head

loss at each flow rate

Table 7: Data needed to calculate hexpand4expfor ball 3al3e (D = " mm)!

#

$%mi

n)

#

(m&%

s)

D

(m)

u

(m%s)Re

'

(cm

"o)

'

(a)

hexp(m)

4exp

4t

heo

htheo(m)

h *

error

4 *

error

00.00

033

2

1.061

571

2205

0.780.7

68.64

655

0.0070

18328

0.122

19

0.

16

0.009

1901

23.63

146

23.631

46

50.00

042

2

1.326

964

2756

3.472

196.1

33

0.0200

52367

0.223

433

0.

16

0.014

3595

-

39.64

53

-

39.645

3

00.00

050

2

1.592

357

3307

6.163.4

333.4

261

0.0340

89024

0.263

775

0.

16

0.020

6777

-

64.85

91

-

64.859

1

5 0.00

058

2

1.857

749

3858

8.86

5.4 529.5

591

0.0541

4139

0.307

79

0.

16

0.028

1446

-

92.36

-

92.368

11


12/21

86 6

00.00

067

2

2.123

142

4410

1.557.5

735.4

988

0.0751

96376

0.327

294

0.

16

0.036

7603

-

104.5

59

-

104.55

9


Figure 1": The relation between the head loss (h) and the flow rate (#) for ball 3al3e (D = " mm)!

Table /: Data needed to calculate hexpand4expfor angle 3al3e (D = 1. mm)!

#

($%mi

n)

#

(m&%

s)

D

(m)

u

(m%s)Re

'

(cm

"o)

'

(a)

hexp(m)

4exp

4t

heo

5.6

htheo(m

)

h *

error

4 *

error

200.00

033

04

1.887

238

2940

1.04

26.32579.

149

0.2636

88624

1.452

571

,

0.544

5972

51.58

098

51.58

098

250.00

042

04

2.359

047

3675

1.2942.8

4197.

246

0.4291

2065

1.512

883

,

0.850

9331

49.57

058

49.57

058

300.00

050

04

2.830

856

4410

1.5562.5

6129.

156

0.6266

36463

1.534

19

,

1.225

3437

48.86

035

48.86

035

350.00

058

04

3.302

666

5145

1.8186.5

8482.

752

0.8672

64865

1.559

989

,

1.667

8289

48.00

037

48.00

037

12


13/21

400.00

067

04

3.774

475

5880

2.07114

1117

9.58

1.1429

84909

1.574

078

,

2.178

3887

47.53

072

47.53

072


Figure 1&: The relation between the head loss (h) and the flow rate (#) for angle seat 3al3e (D = 1. mm)!

Table 0: Data needed to calculate hexpand4expfor Diaphragm 3al3e (D = " mm)!

#

$%mi

)

#

(m&%s

)

D

(m

)

u

(m%s)Re

'

(cm

"o)

'

(a)

hexp(m)

4exp4th5+6

htheo(m)

h *

error

4 *

error

00.00

033

0.

02

1.061

571

2205

0.7815.1

1480.

804

0.15139

537

2.635

806

2,

0.132

1074

-

14.60

02

-

14.60

02

50.00

042

0.

02

1.326

964

2756

3.4725

2451.

663

0.25065

4585

2.792

907

2,

0.206

4178

-

21.43

07

-

21.43

07

00.00

050

0.

02

1.592

357

3307

6.1636.8

3608.

847

0.36896

355

2.854

971

2,

0.297

2416

-

24.12

92

-

24.12

92

5 0.00

058

0.

02

1.857

749

3858

8.86

49.8 4883.

712

0.49930

3934

2.838

505

2,

0.404

5788

-

23.41

-

23.41

13


14/21

33 33

00.00

067

0.

02

2.123

142

4410

1.5567

6570.

456

0.67175

4289

2.923

824

2,

0.528

4295

-

27.12

28

-

27.12

28


Figure 1+: The relation between the head loss (h) and the flow rate (#) for diaphragm 3al3e (D=" mm)!

For the elbows:

Table 1: Data needed to calculate hexpand4expfor 0 elbow (D = ". mm)!

14

($%min)#

(m

&

%s)

D

(m)

u (m%s) Re'

(cm "o)

' (a)hexp

(m)

4exp 5.6 4theo5"6 htheo(

0.00033 24

0.679406 17640.62 1.5 147.0998 0.015039275 0.639246 0.74 0.017

0.00042 24

0.849257 22050.78 3.4 333.4261 0.034089024 0.927332 0.74 0.027

0.00050 24

1.019108 26460.93 6.1 598.2057 0.061159719 1.155377 0.74 0.0391

0.00058 24

1.18896 30871.09 9.2 902.2118 0.092240887 1.280231 0.74 0.053

0.00067 24

1.358811 35281.24 12.5 1225.831 0.125327293 1.331762 0.74 0.069


15/21


Figure 1.: The relation between the head loss (h) and the flow rate (#) for0 elbow (D = ". mm)!

Table 11: Data needed to calculate hexpand4expfor +. elbow (D = ". mm)!

#

($%

min)

#

(m&

%s)

D

(m

)

u

(m%s

)

Re

'

(cm

"o

)

'

(a)

hexp(m)

4exp

4

th

e

5.6

htheo(

m)

h *

erro

r

4 *

erro

r

20

0.0

003

3

24

0.67

940

6

176

40.6

2

0.9

88.2

598

5

0.009

0235

65

0.38

354

7

0

.

3

0.00

7058

-

27.8

491

-

27.8

491

25

0.0

004

2

24

0.84

925

7

220

50.7

8

2.2

215.

746

3

0.022

0576

04

0.60

003

9

0

.

3

0.01

1028

1

-

100.

013

-

100.

013

30

0.0

005

0

24

1.01

910

8

264

60.9

3

3.2

313.

812

8

0.032

0837

87

0.60

61

0

.

3

0.01

5880

5

-

102.

033

-

102.

033

35

0.0

005

8

24

1.18

896

308

71.0

9

6.1

598.

205

7

0.061

1597

19

0.84

884

9

0

.

3

0.02

1615

1

-

182.

95

-

182.

95

15


16/21

40

0.0

006

7

24

1.35

881

1

352

81.2

4

8.9

872.

791

9

0.089

2330

32

0.94

821

4

0

.

3

0.02

8231

9

-

216.

071

-

216.

071


Figure 1-: The relation between the head loss (h) and the flow rate (#) for+. elbow (D = ". mm)!

16


17/21

Determine the discharge coefficient of orifice and venturi meters:

To determine the discharge coefficient for the orifice and venturi meters" the

following equation will -e used


18/21

Ta-le 0, represents the discharge coefficient for the orifice meter at each flow rate"

and the error -etween them

18


19/21

,ample alculation:

For the rough pipe D=17 mm

To find the we calculated from:

.or the first pipe 1 @ 0'mm

For other pipes from mood chart b getting Renolds number and the relati3e

roughness

19


20/21

For the fittings:

For the gate 3al3e D = "& mm

htheor=

Kexp =

20


21/21

For the 3enturi and orifice meter

For the orifice meter:

21

Date post:	03-Jun-2018
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