RESULTS1 lab1

8/11/2019 RESULTS1 lab1

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RESULTS

Table 1: Data measured for the 28 x 1mm Cu pipe (Pipe 1, d=26mm)

Flow rate /m

3

h

-1

Upstreampressure /m

Downstreampressure /m

Pressuredifference (=Head

loss due to

friction, Hf)/m

4.0 0.452 0.205 0.247

3.0 0.378 0.230 0.148

2.0 0.322 0.249 0.073

Flow rate /L h-1 Upstreampressure /m

Downstreampressure /m

Pressuredifference (=Head

loss due to

friction, Hf)/m

500 0.270 0.264 0.006

250 0.267 0.265 0.002


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Table 2: Data measured for the 18 x 1mm Cu pipe (Pipe 2, d=16mm)

Flow rate /m3h

-1 Upstream pressure /m Downstream pressure

/m

Pressure difference

(=Head loss due to

friction, Hf)/m

2 0.570 0.350 0.220

1 0.418 0.143 0.275

Flow rate /L h-1

Upstream pressure /m Downstream pressure

/m

Pressure difference

(=Head loss due to

friction, Hf)/m

500 0.329 0.240 0.089

400 0.300 0.248 0.052

300 0.331 0.271 0.060

100 0.329 0.279 0.050


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Table 3: Data measured for the St galvanized pipe (Pipe 3, d=16mm)

Flow rate /L h-1

Upstream pressure /m Downstream pressure

/m

Pressure difference

(=Head loss due to

friction, Hf)/m

500 0.469 0.224 0.245

400 0.423 0.270 0.153

300 0.396 0.308 0.088

200 0.374 0.335 0.039

Flow rate /m3h

-1 Upstream pressure /m Downstream pressure

/m

Pressure difference

(=Head loss due to

friction, Hf)/m

0.4 0.504 0.190 0.314

d

Table 4: Results calculated for mean velocity (u) and Reynolds number (Re)

Pipe Area of pipe/m2 Volumetric Flow

(Q)/m3s-1

Uniform velocity of

flow (u)/ms-1

Reynolds Number

1 5.31 x 10-4 11.20 x 10-4 2.11 61364.65

8.34 x 10-4 1.57 45659.96

5.56 x 10-4

1.05 30536.91

1.39x 10-4

0.26 7561.52

0.70 x 10 -4 0.13 3780.76

2 2.01 x 10 -4 5.56 x 10-4 2.77 49574.94

2.78 x 10-4

1.38 24697.99

1.39 x 10-4

0.69 12348.99


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1.11 x 10-4 0.55 9843.40

8.34 x 10-5 0.41 7337.81

2.78 x 10-5

0.14 2505.59

3 2.01 x 10-4

1.11 x 10-4

0.55 9843.40

1.39 x 10-4 0.69 12348.99

1.11 x 10-4 0.55 9843.40

8.34 x 10-5

0.41 7337.81

5.56 x 10-5 0.28 5011.19

Table 5: Results calculated for experimental friction factor, theoretical friction factor and Reynolds

number for each pipe

Pipe Head loss due

to friction, Hf

/m

Reynolds

Number

Typical

Roughness

Height (k)/m

Theoretical

Friction Factor

Experimental

Friction Factor

(Darcys Friction

Factor)

1 0.247 61364.65 0.001 x 10-3

0.019904 0.02177

0.148 45659.96 0.021236 0.023561

0.073 30536.91 0.02329 0.025982

0.006 7561.52 0.033433 0.034828

0.002 3780.76 0.04117 0.046438

2 0.220 49574.94 0.020921 0.006924

0.275 24697.99 0.024545 0.03487

0.089 12348.99 0.029241 0.045141

0.052 9843.40 0.031082 0.04151


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0.060 7337.81 0.033743 0.08619

0.050 2505.59 0.047122 0.616013

3 0.245 9843.40 0.1 x 10-3

0.031082 0.195576

0.153 12348.99 0.029241 0.077601

0.088 9843.40 0.031082 0.070248

0.039 7337.81 0.033743 0.056024

0.314 5011.19 0.037746 0.96714

Table 6: Results calculated to plot a graph of log against log Re for each pipe

Pipe Reynolds number,

Re

Log (Re) Theoretical

friction factor

Log( )

1 61364.65 4.787918 0.019904 -1.70106

45659.96 4.659536 0.021236 -1.67293

30536.91 4.484825 0.02329 -1.63283

7561.52 3.878609 0.033433 -1.47582

3780.76 3.577579 0.04117 -1.38542

2 49574.94 4.695262 0.020921 -1.67942

24697.99 4.392662 0.024545 -1.61004

12348.99 4.091631 0.029241 -1.53401

9843.40 3.993145 0.031082 -1.50749

7337.81 3.865566 0.033743 -1.47182

2505.59 3.39891 0.047122 -1.32678

3 9843.40 3.993145 0.031082 -1.50749


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12348.99 4.091631 0.029241 -1.53401

9843.40 3.993145 0.031082 -1.50749

7337.81 3.865566 0.033743 -1.47182

5011.19 3.699941 0.037746 -1.42313

SAMPLE CALCULATIONS

Converting Lh-1to m3h-1

1m3= 1000000 cm

3

But 1L = 1000cm3

1m3= 1000L

1L= 10-3m3 If Q= 600 Lh

-1,

then Q= (600 x 10-3) =0.6m3h-1

Converting m3h

-1to m

3s

-1

1 h= 3600s

1h-1=(1/3600)= 2.78 x 10-4

If Q= 0.6m3h

-1,

Then Q= 0.6 x (2.78 x 10-4

) = 1.67 x 10-4

m3s

-1

Calculating uniform velocity of flow (u) in ms-1

Re: Q= u A

u= Q/A

A= r2= (0.013)

2= 5.31 x 10

-4m

2(For pipe 1)

For Q= 1.67 x 10-4

and A= 5.31 x 10-4

m2,

u= (1.67 x 10-4)/ (5.31 x 10-4)

u= 0.315 ms-1

Calculating Reynolds Number

v

udRe , where v=0.894 x 10-6for water at 25oC

For u=0.315, d=0.026m and v= 0.894 x 10-6

,

07.916110894.0

)026.0)(315.0(Re

6


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Calculating the Theoretical Friction Factor ( )

Recall Haalands Relationship:

11.1

71.3Re

9.6

log8.1

1

d

k

where is the friction factor for the pipe

k is the typical roughness height (m)

Re is Reynolds number

d is the diameter of the pipe

For Cu pipe of diameter 0.026 m, k=0.001 x 10-3

, Re=9161.07

1 = -1.8 log {[6.9/9161.07]+[0.001 x 10-3/3.71(0.026)]1.11}

= -1.8 log {(0.000753) + (0.000010366)1.11}

= -1.8 log (0.000753 + 0.000002933)

=-1.8(-3.12)

=5.616

= 1/(5.616) = 0.178

= (0.178)2= 0.0317

Calculating the Experimental Friction Factor( )Recall Equation to calculate Darcy Friction Factor:

2

2

Lu

gdhf

where L is the length of the pipes under study= 1.3m

hfis head loss due to friction

g is acceleration due to gravity = 9.81 m2s

-1

d is diameter of the pipe

u is the uniform velocity of flow

For hf= 0.025, d= 0.026m, u=0.315 ms-1

= [(0.025)x2(9.81)(0.026)] /[(1.35)(0.315)2]

= (0.012753)/(0.13396)

=0.0952


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Calculating for the Cu (28x1mm) pipe

Average Re= (7619.69 + 9161.07 + 15239.37 + 30536.91 + 45659.96)/ 5

= 21643.4

Using the Haaland Equation,

1

= -1.8 log {(6.9/21643.4) + [(0.001x10-3)/ (3.71)(0.026)]1.11}

= -1.8 log [(3.19x10-4)+ (2.933x10-6)

=-1.8 log (3.22x10-4

)

=-1.8(-3.492)

=6.286

= [1/ (6.286)]2

= (0.159)2

= 0.0253

Average hf=(0.005+ 0.025+ 0.043 + 0.10+ 0.175)/5

=0.0786

Average U= (0.262+ 0.315+ 0.524+ 1.05 +1.57)/5

= 0.744 ms-1

Using equation for the Darcy Friction Factor,

= {(0.0786)(2)(9.81)(0.026)/[(1.35)(0.744)2

]}

= (0.0401)/(0.747)

=0.0537

Calculating for the Cu (18 x 1mm) pipe


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Average Re= (4957.49 + 7409.40 + 9879.19 + 14872.48 + 49574.94)/ 5

= 17338.7


1

= -1.8 log{(6.9/17338.7) + [(0.001X10-3

)/(3.71x 0.016)]1.11

}

= -1.8 log[(3.98x10-4

) + (5.028x10-6

)]

= -1.8 log(4.03x10-4)

= -1.8(-3.395)

=6.111

= [(1/6.111)2]

= (0.164)2

= 0.0269

Average hf= (0.008+ 0.002 +0.031 +0.085 +0.233)/5

= 0.0718

Average U= (0.277 +0.414 +0.552 +0.831 +2.77)/5

= 0.969 ms-1

Using the equation for Darcy Friction Factor,

= {[(0.0718)(2)(9.81)(0.016)]/[(1.35)(0.969)2]}

= (0.0225)/(1.27)

= 0.0177

Calculating for the St galvanized pipe

Average Re= (2469.80 + 4957.49+ 7409.40+ 9879.19 +14872.48)/5

= 7917.7


1

= -1.8 log{(6.9/7917.7) + [(0.1x10-3

)/(3.71 x 0.016)]1.11

}


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= -1.8 log[(8.71x10-4) + (8.344x10-4)]

= -1.8 log(1.71x10-3)

=-1.8(-2.768)

=4.982

= [(1/4.982)2]

= (0.201)2

=0.0404

Using the equation for Darcy Friction Factor,

Average hf= (0.008+ 0.023+ 0.058+ 0.107+ 0.355)/5

= 0.110

Average U= (0.138+ 0.277+ 0.414 + 0.552+ 0.831)/5

= 0.442 ms-1

= {*(0.110)(2)(9.81)(0.016)]/[(1.35)(0.442)2]}

= [(0.0345)/(0.264)]

=0.131


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-1.8

-1.7

-1.6

-1.5

-1.4

-1.3

-1.2

0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

log()

log (Re)

Graph 1 showing logvs log Re for all three pipes

Cu pipe (18x1)

Cu pipe(28x1)

1/2'' St galvanized pipe

-1.8

-1.7

-1.6

-1.5

-1.4

-1.3

-1.2

0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05

log()

log (Re)

Graph 1 showing logvs log Re for Cu pipe (18x1)

Cu pipe (18x1)


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-1.8

-1.7

-1.6

-1.5

-1.4

-1.3

-1.2

0.015 0.02 0.025 0.03 0.035 0.04 0.045

log()

log (Re)

Graph 1 showing logvs log Re for Cu pipe (28x1)

Cu pipe(28x1)

-1.6

-1.55

-1.5

-1.45

-1.4

-1.35

-1.3

-1.25

-1.2

0.015 0.02 0.025 0.03 0.035 0.04

log()

log (Re)

Graph 1 showing logvs log Re for all three pipes

1/2'' St galvanized pipe

Documents

RESULTS1 lab1