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1.0 INTRODUCTION

1.1 Literature Review

Head loss is a measure of the reduction in the total head (sum of elevation head, velocity

head and pressure head) of the fluid as it moves through a fluid system. Head loss is unavoidable

in real fluids.

There are two categories of head loss in pipe. One of them is due to viscous resistance

extending throughout the total length of the circuit. Next is due to localized effects such as

valves, sudden changes in area of flow and bends. Many factors affect the head loss in pipes, the

viscosity of the fluid being handled, the sizes of the pipes, the roughness of the internal surface

of the pipes, the changes in elevation within the system and the length of travel of the fluid.

The resistance through various valves and fittings will also contribute to the overall head

loss. A method to model the resistances for valves and fittings will be of minor significance to

the overall head loss, many designers choose to ignore the head loss for valves and fittings at

least in the initial stages of a design.

Frictional loss is that part of the total head loss that occurs as the fluid flows through

straight pipes. The head loss for fluid flow is directly proportional to the length of pipe, the

square of the fluid velocity, and a term accounting for fluid friction called the friction factor. The

head loss is inversely proportional to the diameter of the pipe.

The friction factor has been determined to depend on the Reynolds number for the flow

and the degree of roughness of the pipe’s inner surface.

1

The overall head loss is a combination of both these categories.

The arrangement of the apparatus is shown in the table below:

Dark Blue Circuit Light Blue Circuit

A) Straight pipe 13.7 mm diameter E) Sudden expansion – 13.6 mm/26.2 mm

B) 90o sharp bend (mitre) 0 mm radius F) Sudden contraction – 26.2 mm/13.6 mm

C) Proprietary 90o elbow 12.7 mm radius G) Smooth 90o bend 50.8 mm radius

D) Gate valve H) Smooth 90o bend 100 mm radius

J) Smooth 90o bend 152 radius

K) Globe valve

L) Straight pipe length 26.4 mm

2

1.2 Theory

Head Loss in Straight Pipe

Darcy-Weisback and Reynold Number equation:

HL=4 fLV ²

2gd = 32 fLQ ²π ² gd ⁵ = KQn

Re= ρVd

μ

f= 64ℜ Laminar flow

f= 0.316×Re -0.25 Turbulent flow

where:

hL= Head losses

f= Friction factor

L= Length

V= Mean velocity (QA )

g= Gravity

d= Constant diameter

3

Head Losses due to Sudden Changes in Area of Flow

I. Sudden Expansion

Expanding pipe

hL= K (V ₁−V ₂)

2 g

Where:

V= Mean velocity

K= Dimensionless coefficient

II. Sudden Contraction

Contracting pipe

hL= KV ₂²

2 g

Where:

K= Dimension coefficient which depends upon the area ratio as shown in Table 1

A1/A2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

K 0.50 0.45 0.41 0.39 0.36 0.33 0.28 0.15 0.15 0.06 0

Table 1 : Loss coefficients for sudden contractions

4

Temperature (oC) ρ (kg/m3) μ (x 10-3 Ns/m2)

0 999.8 1.781

5 1000.0 1.518

10 999.7 1.307

15 999.1 1.139

20 998.2 1.002

25 997.0 0.890

30 995.7 0.798

40 992.2 0.653

50 988.0 0.547

60 983.2 0.466

70 977.8 0.404

80 971.8 0.354

90 965.3 0.315

100 953.4 0.282

Table 2 : Table of ρ and μ depend on temperature.

5

Head Loss due to Bends

hb= KвV ²

2 g

Where:

KB= Dimensionless coefficient which depends upon the bend/ pipe radius ratio and the angle of the bend.

Head Loss due to Valves

hv = Kѵ V ²

2 g

Where:

KV= Dimensionless coefficient which depends upon type of valve and degrees of opening

Valve K

Globe valve, fully open 10.0

Gate valve, fully open 0.2

Gate valve, half open 5.6

Table 3: Values of loss coefficient for gate valve and globe valve

1.3 Objective

1. To find Reynold Number, friction factor and compare with the theoretical value.

2. To find the head loss as a function of volume flow rate.

6

2.0 METHODOLOGY

2.1 Procedure

1. It is important for the globe valve; gate valve and water control valve on the hydraulic bench are fully close. (open-anti-clockwise, close- clockwise)

2. The pump is switched on by pressing the black button on the hydraulic bench and the pump is to let running for a few minutes.

3. The readings on the piezometer tubes (No 1-16) and the U-tube are recorded.

4. The piezometer tubes are identified by fill in Table 1 and refer to Figure 1.

5. The water control valve on the hydraulic bench is opened slowly to check there is no leaking along the pipeline.

6. The water control valve and gate valve are fully-opened to obtain maximum flow through the Dark Blue circuit.

7. Time to collect 15 L of water on the hydraulic bench is recorded. The piezometer (no 1-

6) and U-tube (Gate valve) are read. The temperature of water on the hydraulic bench is

recorded.

8. A half-turn is made on the gate valve and procedure no 6 is repeated.

9. The above procedures are repeated for a total of 8 different valve opening/radings.

10. The gate valve is fully-closed and the globe valve is fully-opened. The same procedures

are repeated for the Light Blue circuit.

11. For globe valve, piezometer is recorded as no. 7-16.

12. Before switching off the pump, the globe valve, gate valve and water control valve are

fully-closed.

7

3.0 RESULTS AND DISCUSSIONS

3.1 RESULTS

TABLE 1: IDENTIFYING PIPING SYSTEM

DARK BLUE CIRCUIT

Pipe description Piezometer tube no.

Straight pipe 13.7mm diameter 3 and 4

90o sharp bend (mitre) 0mm radius 5 and 6

Proprietary 90o elbow 12.7mm radius 1 and 2Table 1

LIGHT BLUE CIRCUIT

Pipe description Piezometer tube no.

Sudden expansion – 13.7mm/26.4mm 7 and 8

Sudden contraction – 26.4mm/13.7mm 9 and 10

Smooth 90o bend 50.8 mm radius 15 and 16

Smooth 90o bend 100 mm radius 11 and 12

Smooth 90o bend 152 mm radius 13 and 14

Straight pipe length 26.4 mm 8 and 9Table 2

8

FOR GATE VALVE

Test

no.

Time

(s)

Piezometer tube readings (cm) waterU-tube (cm)

HgT

(oC)1 2 3 4 5 6 Gate Valve

- 69 690 375 230 15 1050 630 355 365 29

1 78 695 375 230 10 1048 630 355 368 29

2 76 694 373 230 13 1050 630 355 368 29

3 71 693 372 229 13 1050 630 355 368 29

4 68 693 375 229 18 1049 630 355 368 29

5 69 692 378 228 15 1049 633 350 368 29Table 3

FOR GLOBE VALVE

Test

no.

Time

(s)

Piezometer tube readings (cm) waterU-tube (cm)

Hg T (oC)

7 8 9 10 11 12 13 14 15 16 Globe Valve

Initial 72 395 444 432 240 385 135 440 200 385 150 340 330 30

1 65 395 445 433 240 385 135 440 195 385 150 340 330 30

2 63 394 443 430 239 385 130 440 195 385 145 342 326 30

3 64 395 445 434 240 385 130 440 195 386 149 340 326 30

4 65 395 444 433 244 385 140 440 200 385 150 340 332 30

5 65 395 444 433 245 390 140 440 200 385 155 335 333 30Table 4

9

3.2 Discussions

Determination of the coefficient K consists of plotting the experimental local loss

coefficients versus the corresponding Reynolds numbers, Re= VDn , where D is the diameter of

the pipe and n s the kinematic viscosity for known discharges through the device. The head loss

of the devices included in a pipe systems must be determine in order to be used in design

calculations to find the amount of head loss in the system, and consequently, the needed source

pressure or energy to satisfy the design objective.

Determination of the friction factor first requires a value for the head loss to be obtained. The

head loss represents the conversion of mechanical energy to unwanted thermal energy. The

thermal energy is generated as the flow interacts with the surface of the pipe producing heat and

thus producing a pressure loss in the pipe. The pressure loss for the experiment is determined

through the use of a manometer. The manometer reading was a direct measurement of the head

loss that occurred between the two points of interest.

We try to find Reynolds Number and the Friction factor experimentally and compare the

values with the theoretical values in this experiment. We also determined the head loss as a

function of volume flow rate. Thus, our experimental values are not accurate compare to

theoretical values.

The factors that affecting the values of K includes the flow Reynolds number and proximity

to other things which is the tabulated values of K are components in isolation with long straight

runs of pipe upstream and downstream.

There are a few precaution steps in order to get the more accurate result in this experiment.

We must ensure that we read the manual before start the experiment. Before running anything,

we should know how to control the flow in the apparatus. We also have to make sure there are no

bubbles in the pipeline system to eliminate disturbance to the fluid flow. The head loss of the

devices included in a pipe systems must be determine in order to be used in design calculations

to find the amount of head loss in the system, and consequently, the needed source pressure or

energy to satisfy the design objective.

10

3.3 Questions

1. Plot graph of Log10 hL versus Log10 Q on graph paper to get the value of K and n.

Calculate the value of friction factor, f and Reynold number, Re

Head loss, hL in straight pipe, so we use Piezometer 3 and Piezometer 4.

Head loss, hL = Piezometer height 1 – Piezometer height 2

Volume flow rate,

Q=VolumeTime

Q (m3/s)(x10-4) Log10Q hL (m) Log10hL

1.923 -3.716 2.20 0.342

1.974 -3.705 2.17 0.336

2.113 -3.675 2.16 0.334

2.206 -3.656 2.11 0.324

2.174 -3.663 2.13 0.328Table 5

-3.716 -3.705 -3.675 -3.656 -3.6630.315

0.320

0.325

0.330

0.335

0.340

0.345Graph of Log10 hL vs Log10 Q

Log10 Q

Log1

0 hL

Graph 1

11

Due some unforeseen error, the result obtained is not accurate. Hence the graph is not linear.

To assume the gradient of graph, the first and last point is taken into calculation.

Gradient of graph, m =

y 2− y 1

x 2−x 1

=

0 .342−0 .328−3 .716−(−3 .663 )

= -0.264

Y= mX + c

hL = KQn

log hL = log K + n log Q

n = m

thus, n = -0.264

log hL = log K + n log Q

0.342 = Log K + (-0.264) (-3.716)

Log K = -0.639

K = 2.3×10-1

13

Velocity,

V=QA

= Q

πr ²

Reynolds Number, Re=

ρVdμ

For ρ,

From table 2 in module,

Temperature (°C) ρ (kg/ m3)

25 997.0

29 ρ

30 995.7

Table 6

ρ−997.0995.7−997.0 =

29−2530−25

ρ = 995.96 kg/m3

For μ,

From table 2 in module,

Temperature (°C) μ(×10-3 Ns/ m2)

25 0.890

29 μ

30 0.798

Table 7

μ−0.8900.798−0.890 = 29−25

30−25

14

μ= 0.8164 ×10-3 Ns/ m2

Friction factor,

f =

64Re (Laminar flow)

f = 0.316 x Re-0.25 (Turbulent flow)

Table 8

15

Velocity, v (m/s) Reynolds number, Re Type of Flow Fiction factor, f (x10-3)

1.304 21794 Turbulent 26.0

1.339 22379 Turbulent 25.8

1.433 23950 Turbulent 25.4

1.496 25003 Turbulent 25.1

1.475 24652 Turbulent 25.2

2. Plot graph of hL versus (V1- V2)2/ 2g for Sudden Expansion Pipe to get the K value and compare with the theoretical value, K=1.0. Calculate the error.Head loss, hL for Sudden Expansion Pipe, so we use Piezometer 7 and Piezometer 8.


Volume flow rate,

Q=VolumeTime

Velocity,

V=QA

Q (m3/s)(x10-4) hL (m) V1 (m/s) V2 (m/s) (V1-V2)2/2g (m)

2.308 0.50 1.566 0.422 0.067

2.381 0.49 1.615 0.435 0.071

2.344 0.50 1.590 0.428 0.069

2.308 0.49 1.566 0.422 0.067

2.308 0.49 1.566 0.422 0.067

Table 9

0.0665 0.067 0.0675 0.068 0.0685 0.069 0.0695 0.07 0.0705 0.071 0.07150.484

0.486

0.488

0.49

0.492

0.494

0.496

0.498

0.5

0.502

Graph of hL vs (V1- V2)2/ 2g

(V1- V2)2/ 2g (m)

hL (m

)

16

Graph 2

17

Due some unforeseen error, the result obtained is not accurate. Hence the graph is not linear. To

assume the gradient of graph, only two points are taken into calculation.

Gradient of graph, m = y₂− y₁x₂−x₁

= 0.49−0.50

0.071−0.067

= -2.5

hL=K(V 1−V 2)

2

2 g

Y= mX+ c

Therefore, m= K

Hence, K= -2.5

Calculated K value is smaller than theoretical K value.

Error = 1.0−(−2.5 )

1 .0×100 %

= 350%

18

3. Plot graph of hL versus (V2)2/ 2g for Sudden Contraction pipe to get the K value and

compare with the theoretical value, K= 0.30. Calculate the error.

Head loss, hL for Sudden Expansion Pipe, so we use Piezometer 9 and Piezometer 10.


Volume flow rate,

Q=VolumeTime Velocity,

V=QA

Q (m3/s)(x10-4) hL (m) V2 (m/s) (V2)2/2g (m)

2.308 1.93 1.566 0.125

2.381 1.91 1.615 0.133

2.344 1.94 1.590 0.129

2.308 1.89 1.566 0.125

2.308 1.88 1.566 0.125

Table 10

0.124 0.125 0.126 0.127 0.128 0.129 0.13 0.131 0.132 0.133 0.1341.84

1.86

1.88

1.9

1.92

1.94

1.96

Graph of hL vs (V2)2/ 2g

(V2)2/ 2g (m)

hL (m

)

19

Graph 3

20




= 1.94−1.930.129−0.125

= 2.5

hL=KV

22

2g

Y= mX+ c

Therefore, m= K

Hence, K= 2.5

Calculated K value is larger than theoretical K value.

Error =

2. 5−0. 300 .30

×100 %

= 733.33%

21

4. Plot graph of hL versus V2/ 2g for Bending pipe to get the value of K and compare with

the theoretical value, K= 0.37. Calculate the error.

For proprietary 90o elbow 12.7mm radius, we use Piezometer 1 and Piezometer 2.


Volume flow rate,


V=QA

Q (m3/s)(x10-4) hL (m) V (m/s) V2/2g (m)

1.923 3.20 1.518 0.117

1.984 3.21 1.566 0.125

2.101 3.21 1.659 0.140

2.212 3.18 1.746 0.155

2.174 3.14 1.716 0.150

Table 11

0.115 0.12 0.125 0.13 0.135 0.14 0.145 0.15 0.155 0.163.1

3.12

3.14

3.16

3.18

3.2

3.22

Graph of hL vs V2/ 2g

V2/ 2g (m)

hL (m

)

22

Graph 4




= 3.21−3.200.140−0.117

= 0.435

hL=K V 2

2g

Y= mX+ c

Therefore, m= K

Hence, K= 0.435

Calculated K value is larger than theoretical K value.

Error =

0 .435−0 . 370.37

×100 %

= 17.57%

23

For smooth 90o bend 50.8 mm radius, we use Piezometer 15 and Piezometer 16.


Volume flow rate,


V=QA

Q (m3/s)(x10-4) hL (m) V (m/s) V2/2g (m) (x10-4)

2.315 2.35 0.114 6.624

2.381 2.40 0.117 6.977

2.358 2.37 0.116 6.858

2.315 2.35 0.114 6.624

2.284 2.30 0.113 6.508

Table 12

6.4 6.5 6.6 6.7 6.8 6.9 7 7.12.24

2.26

2.28

2.3

2.32

2.34

2.36

2.38

2.4

2.42


V2/ 2g (×10-4) (m)

hL (m

)

24

Graph 5




= 2.37−2.356.858−6.624

= 0.085

hL=K V 2

2g

Y= mX+ c

Therefore, m= K

Hence, K= 0.085


Error =

0 .37−0 . 0850 . 37

×100 %

= 77.0%

25

For smooth 90o bend 100 mm radius, we use Piezometer 11 and Piezometer 12.


Volume flow rate,


V=QA

Q (m3/s)(x10-4) hL (m) V (m/s) V2/2g (m) (x10-4)

2.315 2.50 0.029 4.286

2.381 2.55 0.030 4.587

2.358 2.55 0.030 4.587

2.315 2.45 0.029 4.286

2.284 2.50 0.029 4.286

Table 13

4.25 4.3 4.35 4.4 4.45 4.5 4.55 4.6 4.652.4

2.42

2.44

2.46

2.48

2.5

2.52

2.54

2.56


V2/ 2g (×10-4 ) (m)

hL (m

)

Graph 6

26




= 2.55−2.504.587−4.286

= 0.166

hL=K V 2

2g

Y= mX+ c

Therefore, m= K

Hence, K= 0.166


Error =

0 .37−0 .1660 . 37

×100 %

= 55.0%

28

For smooth 90o bend 152 mm radius, we use Piezometer 13 and Piezometer 14.


Volume flow rate,


V=QA

Q (m3/s)(x10-4) hL (m) V (m/s) V2/2g (m) (x10-6)

2.315 2.45 0.0128 8.35

2.381 2.45 0.0131 8.75

2.358 2.45 0.0130 8.61

2.315 2.40 0.0128 8.35

2.284 2.40 0.0126 8.09

Table 13

8 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.82.37

2.38

2.39

2.4

2.41

2.42

2.43

2.44

2.45

2.46

Graph of hL vs V2/2g

V2/ 2g (×10-6 ) (m)

hL (m

)

Graph 7

29




= 2.40−2.458.09−8.35

= 0.19

hL=K V 2

2g

Y= mX+ c

Therefore, m= K

Hence, K= 0.19


Error =

0 .37−0 .190 .37

×100 %

= 48.6%

31

5. Plot graph of hL versus V2/ 2g for loss due to valves to get the value of K.

For gate valves,


Volume flow rate,


V=QA

Q (m3/s)(x10-4) hL (m) V (m/s) V2/2g (m)

1.923 0.13 1.305 0.0868

1.984 0.13 1.346 0.0923

2.101 0.13 1.425 0.1035

2.212 0.13 1.501 0.1148

2.174 0.18 1.841 0.1727

Table 14

32

0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.180

0.020.040.060.080.1

0.120.140.160.180.2


V2/ 2g (m)

hL (m

)

Graph 8




= 0.18−0.130.1727−0.0923

= 0.62

hL=K V 2

2g

Y= mX+ c

Therefore, m= K

Hence, K= 0.62

33

For globe valve,


Volume flow rate,


V=QA

Q (m3/s)(x10-4) hL (m) V (m/s) V2/2g (m) (×10-3)

2.315 0.10 0.423 9.120

2.381 0.16 0.435 9.644

2.358 0.14 0.431 9.468

2.315 0.08 0.423 9.120

2.294 0.02 0.419 8.948

Table 15

8.9 9 9.1 9.2 9.3 9.4 9.5 9.6 9.70

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18


V2/ 2g (×10-3) (m)

hL (m

)

Graph 9

35




= 0.16−0.109.644−9.120

= 0.115

hL=K V 2

2g

Y= mX+ c

Therefore, m= K

Hence, K= 0.115

36

4.0 Conclusion

The K values obtained from the experiment deviates greatly from the theoretical value of K. It is

shown that head loss is affected by volume flow rate and there is a specific relationship between

them. Therefore, precaution is essential to reduce error in the experiment.

37

5.0 References

http://www.engineeringtoolbox.com/total-pressure-loss-ducts-pipes-d_625.html

http://me.queensu.ca/courses/MECH441/losses.htm

http://www.kmisystemsinc.com/files/Technical%20References/PressureLoss.pdf

Gupta, R. S. (1989). Hydrology and Hydraulic Systems, Waveland Press, NY

Rouse, H. (1949). Engineering Hydraulics, John Wiley and Sons, NY

White, F.M. (1994). Fluid Mechanics, 3rd edition, McGraw-Hill, Inc., New York, NY.

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