1.1 Literature Review

1.0 INTRODUCTION

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.

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

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

1 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

1.2 Theory

Head Loss in Straight Pipe

Darcy-Weisback and Reynold Number equation:

n HL= = = KQ

f= Laminar flow

-0.25 f= 0.316×Re Turbulent flow

where:

2 hL= Head losses f= Friction factor

L= Length

V= Mean velocity () g= Gravity d= Constant diameter

3 Head Losses due to Sudden Changes in Area of Flow

I. Sudden Expansion

Expanding pipe

Where:

V= Mean velocity

K= Dimensionless coefficient

II. Sudden Contraction

Contracting pipe

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

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

4 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=

Where:

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

Head Loss due to Valves hv =

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 2 Table 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 9 Table 2

8 FOR GATE VALVE U-tube (cm) T Test Time Piezometer tube readings (cm) water Hg (oC) no. (s) 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 29 Table 3

FOR GLOBE VALVE U-tube (cm) Test Time Piezometer tube readings (cm) water T (oC) Hg no. (s) 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 30 Table 4

9 3.2 Discussions

Determination of the coefficient K consists of plotting the experimental local loss coefficients versus the corresponding Reynolds numbers, Re= , 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,

3 -4 Q (m /s)(x10 ) 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 0.328 Table 5

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 =

= -0.264

Y= mX + c

n hL = KQ 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

Velocity,

Reynolds Number,

For ρ,

From table 2 in module,

Temperature (°C) ρ (kg/ m3) 25 997.0 29 ρ 30 995.7 Table 6

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= 0.8164 ×10-3 Ns/ m2

Friction factor,

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

13 1.496 25003 Turbulent 25.1

1.475 24652 Turbulent 25.2 f = (Laminar flow)

-0.25 f = 0.316 x Re (Turbulent flow)

Table 8

14 2 2. Plot graph of hL versus (V1- V2) / 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.

Head loss, hL = Piezometer height 1 – Piezometer height 2 Volume flow rate, Velocity,

3 -4 2 Q (m /s)(x10 ) hL (m) V1 (m/s) V2 (m/s) (V1-V2) /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

Table 9

Graph 2

15 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.

= -2.5

Y= mX+ c

Therefore, m= K

Hence, K= -2.5

Calculated K value is smaller than theoretical K value.

Error =

= 350%

16 2 3. Plot graph of hL versus (V2) / 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.

3 -4 2 Q (m /s)(x10 ) hL (m) V2 (m/s) (V2) /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

Graph 3

Y= mX+ c

Therefore, m= K

Hence, K= 2.5

Calculated K value is larger than theoretical K value.

Error =

= 733.33%

18 2 4. Plot graph of hL versus V / 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.

3 -4 2 Q (m /s)(x10 ) hL (m) V (m/s) V /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

Graph 4

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.

= 0.435

Y= mX+ c

Therefore, m= K

Hence, K= 0.435

19 Calculated K value is larger than theoretical K value.

Error =

= 17.57%

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

3 -4 2 -4 Q (m /s)(x10 ) hL (m) V (m/s) V /2g (m) (x10 )

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

Graph 5

= 0.085

Y= mX+ c

Therefore, m= K

Hence, K= 0.085

21 Error =

= 77.0%

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

3 -4 2 -4 Q (m /s)(x10 ) hL (m) V (m/s) V /2g (m) (x10 )

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

Graph 6

= 0.166

Y= mX+ c

Therefore, m= K

Hence, K= 0.166

Error =

= 55.0%

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

3 -4 2 -6 Q (m /s)(x10 ) hL (m) V (m/s) V /2g (m) (x10 )

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

Graph 7

= 0.19

Y= mX+ c

Therefore, m= K

Hence, K= 0.19

Error =

= 48.6%

26 2 5. L Plot graph of h versus V / 2g for loss due to valves to get the value of K.

For gate valves,

3 -4 2 Q (m /s)(x10 ) hL (m) V (m/s) V /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

Graph 8

= 0.62

27 Y= mX+ c

Therefore, m= K

Hence, K= 0.62

28 For globe valve,

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

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

Graph 9

= 0.115

Y= mX+ c

Therefore, m= K

29 Hence, K= 0.115

30 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.

31 5.1 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.