Fluid Mechanics 230Laboratory 2:

Flow Through Pipes Experiment Report

I hereby declare that the report submitted are entirely my own work and have not been copied

from any other student or past year reports.

Name : Wong Yee Jing

Student ID : 7E1b9107 / 15880909

Course : Bachelor of Chemical Engineering

Date Performed : 23 May, 2014 (2-4pm, Friday)

Date Due : 6 June, 2014

Date Submitted : 6 June, 2014

Lecturer : Dr. Sharul Sham Bin Dol

pg. 1

Contents1.0 Introduction....................................................................................................................................

1.1 Theory............................................................................................................................................

2.0 Experimental Procedure...............................................................................................................

2.1 Apparatus used.............................................................................................................................

2.2 Procedure.....................................................................................................................................

3.0 Results..........................................................................................................................................

4.0 Analysis and Discussion................................................................................................................

4.1 Piezometer head...........................................................................................................................

4.2 Development length.....................................................................................................................

4.3 Friction Factor...............................................................................................................................

4.4 Velocity Profile..............................................................................................................................

4.5 Discharge calculation method......................................................................................................

4.6 Assessment of Error......................................................................................................................

5.0 Conclusion....................................................................................................................................

6.0 References....................................................................................................................................

7.0 Appendices...................................................................................................................................

pg. 2

List of TablesTable 1: Properties of fluid and pipe of the experiment -------------------------------------------13

Table 2: Discharge and average velocity-------------------------------------------------------------13

Table 3: Traverse of Test 1 and Test 2----------------------------------------------------------------13

Table 4: Traverse of Test 3 and Test 4----------------------------------------------------------------13

Table 5: Manometer Reading and Calculated Piezometer Head at Various Positions in Pipe

for Test 1, Test 2 and Test 3----------------------------------------------------------------------------14

Table 6: Manometer Reading and Calculated Piezometer Head at Various Positions in Pipe

for Test 4, Test 5 and Test 6----------------------------------------------------------------------------15

Table 7: Average velocity, Reynolds Number, flow type and development length for

Test 1, 2 and 3--------------------------------------------------------------------------------------------17

Table 8: Development length in terms of D----------------------------------------------------------18

Table 9: Static head, head loss and friction factors for test 1 to 4---------------------------------19

Table 10: Experimental and theoretical friction factor and Reynolds number------------------19

Table 11: ΔH for test 1 to 4----------------------------------------------------------------------------21

Table 12: Radius and velocity of each radius point for test 1 to 4--------------------------------21

pg. 3

List of FiguresFigure 1(a) Experiment to illustrate type of flow and; (b) Typical dye streaks-------------------6

Figure 2(a): Laminar flow; (b): Transitional flow; (c): Turbulent ---------------------------------7

Figure 3: Velocity profile and boundary layers in pipes (Dr Andrew Sleigh 2009) -------------8

Figure 4: Laboratory equipment of flow through pipes --------------------------------------------11

Figure 5: Graph plotted of Piezometric Head Versus Piezometric Position---------------------16

Figure 6: Inviscid core and boundary layer of entrance length (Entrance length 2005) -------18

Figure 7: Moody chart ----------------------------------------------------------------------------------

20

Figure 8: Graph of radius versus velocity profile ---------------------------------------------------22

Figure 9: Graph of ΔH (m) against velocity profile(m/s) ------------------------------------------

22

pg. 4

1.0 Introduction

The design of this experiment is to explore the study of flow in pipes. Types of flow

in pipes are classified into three types which are laminar, transitional and turbulent flow.

Transitional regime between laminar and turbulent flow will be identified as well in the

experiment. Pressure gradient along the pipe was measured and the pipe’s fraction factor also

was assessed for different flow rates. Furthermore, velocity profile in the cross section of the

pipe was determined as well in the experiment.

The aim of this experiment was to identify typical laminar, transitional, and turbulent

values of Reynolds Number for flow in a pipe with a circular cross-section. Moreover,

application of friction concept in pipe flow was studied in the experiment. To acquire the

developed flow friction factor for a range of different flows is another objective of the

experiment. Lastly, the velocity profile in both laminar and turbulent flows in a pipe with a

circular cross-section was investigated and compared.

pg. 5

1.1 Theory

Laminar, Transitional or Turbulent flow

The flow in pipes can be either be laminar or turbulent flow. Types of flow can be

determined by Reynolds Number. A British scientist and mathematician who called Osborne

Reynolds was the first to discover the difference between two classifications of flow by using

a simple apparatus as shown in Figure 1(a) below.

Figure 1(a) Experiment to illustrate type of flow and; (b)Typical dye streaks

(Viscous flow in pipes 2014)

If water flows through a pipe of diameter D with a mean velocity V, the following

characteristics of fluid can be observed by injecting a dye as shown in Figure 1(a). When the

flow rate is small enough, the dye streak-line will remain as well. As defined line flows along

with a larger intermediate flow rate, the dye streak-line will fluctuate in time and space.

While for the flow rate is large enough, the dye streak-line changes to become blurred and

spreads across the pipe with random pattern. The three characteristics are known as laminar,

transitional and turbulent flow as illustrated in Figure 1(b).

For laminar flow, it has regular, smooth and systematic flow pattern (refer Figure

2(a)). Low velocity, no intermixing of fluid particles in adjacent layers and high viscosity are

the characteristics of laminar flow. For transitional flow, it displays characteristics of both

turbulent and laminar flow. The laminar flow is near the edge of fluid, while the centre of

fluid is taken by turbulent flow. Transitional flow also is hard to measure same as turbulent

flow. Whereas for turbulent flow, it is irregular and unsteady type of flow.

pg. 6

So, it does have high velocity and low viscosity. The pattern flow for three different types of

flow is illustrated in Figure 2(a), (b) and (c) below.

Figure 2 (a): Laminar flow Figure 2 (b): Transitional flow Figure2(c):Turbulent flow

(Types of flow 2014) (Types of flow 2014) (Types of flow 2014)

Reynolds Number

Reynolds number, Re is a dimensionless parameter which denotes the ratio of the inertia to

viscous effects in the flow. The formula of Reynolds number is shown as follows.

ℜ= ρV Dμ

=V Dv Equation 1

where ρ= density of fluid ;

V= average velocity in pipe;

D= diameter of pipe;

μ= dynamic viscosity of fluid;

v= kinematic viscosity of fluid

The actual transition from laminar to turbulent flow may take place at various

Reynolds number, depending on how much the flow disturbance caused by vibrations in the

pipe and roughness of the entrance region. Generally, flow in a circular cross section is

laminar if the Reynolds number is less than approximately 2100. The flow in a round pipe is

turbulent if the Reynolds number is larger than approximately 4000. For Reynolds number

between these two limits, it is transitional flow which can switch between laminar and

turbulent flow.

Velocity profile, boundary layers, entrance length and fully-developed flow

The types of flow either is laminar or turbulent flow also can depends on the shape of

the velocity profile in pipe. Velocity profile of laminar flow is parabolic which is parallel to

pg. 7

boundary while velocity profile of turbulent flow is known as fuller as chaotic fluctuations

observed. If only the parabolic of laminar flow is found in pipe, the first part of the boundary

layer growth diagram is used as shown in the top diagram of the below Figure 3. If turbulent

(or transitional), both the laminar and turbulent (transitional) regions of the boundary layer

growth diagram are used as shown in bottom diagram of below Figure 3. When boundary

layer has reached the centre of the pipe, the flow is said to be fully-developed. Entry length

which means the length of pipe before fully-developed flow is reached is different for the two

types of flow. The entrance length is quite short for the low Reynolds number whereas for

high Reynolds number, the length is equal to many pipe diameters before the end of entrance

region is reached.

Figure 3: Velocity profile and boundary layers in pipes (Dr Andrew Sleigh 2009)

In this experiment, the velocity profile can be determined from experimental data by

using the Equation 2 shown as below.

V=√2 g∆h Equation 2

where ∆ h is the difference between TP1 and TP2, converted into head of oil.

pg. 8

Head loss in a developed flow

Head loss due to wall shear in a developed flow has a relationship with friction factor as

shown by Darcy-Weisbach equation below. Darcy formula is mainly used to calculate

pressure loss in a pipe due to turbulent flow. Shear stress in a flow is dependent on the flow

either is laminar or turbulent. Pressure drop for turbulent flow is dependent on roughness of

surface due to the fact that a thin viscous layer is formed near to pipe surface in turbulent

flow that causes energy loss. In the case of laminar flow, Poiseuille’s Equation is used as it

determines the pressure drop of a constant viscosity fluid exhibiting laminar flow through a

pipe also shown as below. Pressure drop in laminar flow is vice-versa since roughness effects

of wall are negligible non-existence of viscous layer.

hL=f LDV 2

2 g(Darcy−Weisbach ) Equation 3

hL=32 μLD2

Vρg

(Poiseuill e ' s Equation) Equation 4

where hL=head loss due to friction;

f = friction factor;

L= Pipe length (distance between two piezometer points);

D= Internal diameter pipe;

V= Average flow velocity;

g = gravitational acceleration;

μ=dynamic viscosity;

ρ= density

In this experiment, head loss, hL can be calculated by using Bernoulli’s equation as shown as

formula below.

P1

ρg+V 1

2

2 g+z1=

P2

ρg+V 2

2

2g+z2+hL Equation 5

The Bernoulli’s Equation can be defined in term of head as shown below.

Static head – first term

pg. 9

Dynamic head – second term

Hydrostatic head – third term which represents pressure change due to elevation

Stagnation head – total pressure

Since V 12=V 2

2∧z1=z2, the head loss can be determined.

Friction factor and Moody chart

Friction factor or flow coefficient is depends on parameters of pipe and velocity of fluid flow

but it can be determined accurately within some regimes. It may be evaluated for given

conditions by using numerous empirical or theoretical relations, or it also can be obtained

based on published chart by referring to Moody chart or diagram. The Darcy friction factor

for laminar flow (Re<2100) is given as formula below.

f=64ℜ (laminar flow friction) Equation 6

For friction factor in turbulent flow in smooth pipes, Balsius equation is used as it is the

simplest equation to compute Darcy friction factor. The Balsius correlation is accurate within

± 5% for smooth pipes at Reynolds number less than 100000 (Head Loss Due To Friction In

Circular Pipe 2014). Balsius equation for turbulent flow is given as formula below.

f=λ=0.316ℜ1 /4 (turbulent flow friction) Equation 7

Moody chart is a graph of the friction factor f against Reynolds numbers for various values of

kd , where k is a measure of the wall roughness and d is the pipe diameter. For high

kd values

or high Reynolds number, appropriate kd and Reynolds number on chart should be used. If

the pipe roughness kd is less than 0.01, Balsius equation is used.

pg. 10

2.0 Experimental Procedure2.1 Apparatus used

Figure 4: Laboratory equipment of flow through pipes

The fluid that used in this experiment which was oil was circulated in the circuit of

the apparatus by using gear pump as shown in Figure 4. Oil was drained from the reservoir

and transported by way of the lower horizontal pipe. Then, the oil moved from this chamber

through a parabolic bell mouth into a brass pipe of 19mm bore and overall length 4.4m, with

18 pizeometric tappings along its length.

The pipe was discharged to the atmosphere so that the difference on types of flow can

be observed. Typicall, lower discharge will generate a laminar flow. A flow disturber was

inserted at the upstream end of the pipe at lower flow rates to produce a turbulent flow for

lower where its Reynolds number is approximately 5000.

A pitot tube (TP1-Channel 19) that can be traversed across the flow in the pipe was

situated at the downstream end of the pipe adjacent to a static tapping (TP2-Channel 17). The

recorded readings can be used to determine the flow speed.

pg. 11

2.2 Procedure

Test 1-3: Turbulent and Laminar Flow Conditions

The control valve was checked to be shut and the flow disturber was fully retracted.

The pump was started and control valve was opened slowly until a minimum flow rate of

18L/min was reached. The reading of discharge and all manometer readings were recorded.

The readings of pitot tube (TP1) and static tube (TP2) for different locations along the cross

section of the pipe were recorded. Steps 3 and 4 were repeated with the increased flow rates

that give 26L/min and 30L/min respectively.

Test 4: Transitional Flow Condition

The flow disturber was retracted. The flow rate was increased until the flow condition

was transitional flow. All manometer readings (1-19) were recorded and the discharge was

measured. The readings of pitot tube (TP1) and static tube (TP2) for different locations along

the cross section of the pipe were recorded.

Test 5-6: With and without flow disturber

The flow rate was adjusted to 18 L/min and the condition was checked for laminar

flow. All the manometer readings were recorded. Flow disturber was inserted without

changing the flow rate. All the manometer readings were recorded again and the discharge

was measured as well.

After the experiment was fully carried out, the control valve was closed and pump was

checked to be stopped.

pg. 12

3.0 Results

Properties of fluid (oil) and pipe:

Density of oil, 𝜌 (Kg/m3) 841Kinematic viscosity of oil, 𝜇 (m2/s) 7.7x10-6 @20℃

Diameter of pipe, 𝐷 (m) 0.019Roughness of pipe wall,k s(m) 0.0015

Table 3: Properties of fluid and pipe of the experiment

Discharge:

Test No. Discharge (L/min) Discharge (m3/s) Average Velocity (m/s)

Test 1 18 3.00 x10-4 1.058Test 2 26 4.33 x10-4 1.527Test 3 30 5.00 x10-4 1.764Test 4 22 3.67 x10-4 1.295

Test 5 & 6 18 3.00 x10-4 1.058Table 4: Discharge and average velocity

*Please refer to Appendix I for calculations of discharge and average velocity.

Traverse results:

Rod reading (mm)

Distance from wall (mm)

Test 1 Pressure (bar)

Test 2 Pressure (bar)

TP1 TP2 TP1 TP216.5 1.0 0.033 0.027 0.047 0.03414.5 3.0 0.039 0.027 0.050 0.03412.5 5.0 0.043 0.026 0.052 0.03210.5 7.0 0.044 0.026 0.054 0.0329.0 8.5 0.043 0.025 0.052 0.0328.0 9.5 0.041 0.025 0.052 0.032

Table 3: Traverse of Test 1 and Test 2

Rod reading (mm)

Distance from wall (mm)

Test 3 Pressure (bar)

Test 4Pressure (bar)

TP1 TP2 TP1 TP216.5 1.0 0.052 0.036 0.039 0.02714.5 3.0 0.055 0.036 0.048 0.02712.5 5.0 0.057 0.035 0.050 0.02610.5 7.0 0.058 0.034 0.052 0.0269.0 8.5 0.058 0.034 0.050 0.0258.0 9.5 0.057 0.034 0.049 0.025

Table 4: Traverse of Test 3 and Test 4

pg. 13

Piezometer Head:

Manometer No Position (m)

Test 1 Test 2 Test 3

P (bar) H (m) P (bar) H (m) P (bar) H (m)

1 0.160 0.058 0.7030 0.102 1.236 0.128 1.551

2 0.300 0.056 0.6788 0.100 1.212 0.124 1.503

3 0.450 0.045 0.5454 0.089 1.079 0.113 1.370

4 0.600 0.052 0.6303 0.095 1.151 0.121 1.467

5 0.750 0.049 0.5939 0.091 1.103 0.115 1.394

6 0.900 0.046 0.5576 0.088 1.067 0.116 1.406

7 1.050 0.041 0.4970 0.083 1.006 0.108 1.309

8 1.200 0.045 0.5454 0.086 1.042 0.109 1.321

9 1.350 0.043 0.5212 0.082 0.9939 0.104 1.261

10 1.500 0.042 0.5091 0.083 1.006 0.102 1.236

11 1.800 0.040 0.4848 0.075 0.9091 0.095 1.151

12 2.100 0.038 0.4606 0.073 0.8848 0.087 1.055

13 2.400 0.034 0.4121 0.067 0.8121 0.079 0.9576

14 2.750 0.033 0.4000 0.058 0.7030 0.069 0.8363

15 3.160 0.030 0.3636 0.051 0.6182 0.058 0.7030

16 3.610 0.028 0.3394 0.043 0.5212 0.045 0.5454

17 3.930 0.025 0.3030 0.032 0.3879 0.034 0.4121

18 4.195 0.023 0.2788 0.027 0.3273 0.029 0.3515

19 3.950 0.022 0.2667 0.047 0.5697 0.052 0.6303

Table 5: Manometer Reading and Calculated Piezometer Head at Various Positions in Pipe for Test 1, Test 2 and Test 3

pg. 14

Manometer No Position (m)

Test 4Test 5

Without flow disturber

Test 6 With flow disturber

P (bar) H (m) P (bar) H (m) P (bar) H (m)

1 0.160 0.061 0.7394 0.058 0.7030 0.059 0.7151

2 0.300 0.058 0.7030 0.056 0.6788 0.058 0.7030

3 0.450 0.047 0.5697 0.045 0.5454 0.048 0.5818

4 0.600 0.055 0.6667 0.052 0.6303 0.056 0.6788

5 0.750 0.051 0.6182 0.049 0.5939 0.052 0.6303

6 0.900 0.052 0.6303 0.046 0.5576 0.052 0.6303

7 1.050 0.045 0.5454 0.041 0.4970 0.047 0.5697

8 1.200 0.048 0.5818 0.045 0.5454 0.050 0.6060

9 1.350 0.046 0.5576 0.043 0.5212 0.048 0.5818

10 1.500 0.045 0.5454 0.042 0.5091 0.047 0.5697

11 1.800 0.043 0.5212 0.040 0.4848 0.045 0.5454

12 2.100 0.041 0.4970 0.038 0.4606 0.043 0.5212

13 2.400 0.038 0.4606 0.034 0.4121 0.037 0.4485

14 2.750 0.036 0.4364 0.033 0.4000 0.036 0.4364

15 3.160 0.032 0.3879 0.030 0.3636 0.033 0.3999

16 3.610 0.030 0.3636 0.028 0.3394 0.029 0.3515

17 3.930 0.024 0.2909 0.025 0.3030 0.024 0.2909

18 4.195 0.023 0.2788 0.023 0.2788 0.023 0.2788

19 3.950 0.037 0.4485 0.022 0.2667 0.031 0.3757

Table 6: Manometer Reading and Calculated Piezometer Head at Various Positions in Pipe for Test 4, Test 5 and Test 6

pg. 15

4.0 Analysis and Discussion4.1 Piezometer head

0 0.5 1 1.5 2 2.5 3 3.5 4 4.50

0.20.40.60.8

11.21.41.61.8

Graph of Piezometric Head (m) Versus Piezometric Position (m)

Test 1Test 2Test 3Test 4Test 5Test 6

Piezometric Position (m)

Piez

omet

ric H

ead

(m)

Figure 5: Graph plotted of Piezometric Head Versus Piezometric Position

Based on Figure 5, it is a negative gradient graph for all the tests which indicates that

pizezometric head is inversely proportional to piezometric position. When piezometric head

decreases, piezometric position increases. The pressure drop is caused by the friction which

also known as shear stress happens between the wall and fluid. This is based on the concept

of conservation of energy which tells that energy losses in the pipe can cause pressure drop

occurred across the pipe. The friction occurred due to the viscous effects of fluid. Shear stress

is related with pressure drop as can be shown by analytical expression as shown below

(Laminar and Turbulent flows in pipes 2014).

τ=∆ PL

r2

This analysis is valid for both laminar and turbulent flows. The total shear stress for both

laminar and turbulent flows is different. The apparent shear stress for turbulent flows are

much greater than laminar flows. This is due to the eddy viscosity which is not a simple

property fluid and varies from one point to another point or from one flow to another

condition. Compared to others, Test 3 has the highest pressure gradient with the highest

average velocity due to resulted higher shear stress. Test 1 has the lowest pressure gradient

and lowest average velocity due to lower shear stress experienced. Between Test 5 and Test

6, Test 6 does have a higher pressure gradient as with the presence of flow disturber that

helps in the development of turbulent flow in laminar flow. The flow is disturbed and hence

pg. 16

the fluctuations increase. As a result, pressure gradient and average velocity increase due to

increased shear stress.

4.2 Development lengthThe length required to achieve a fully-developed flow is known as development

length. To calculate development length for laminar and turbulent flows, the equations are

shown respectively.

¿D

=0.058ℜ(Laminar flow ) Equation 8

¿D

=4.4 (ℜ)16 (Turbulent flow ) Equation 9

Reynolds number and development length are determined and tabulated as shown in table below.

Test Average Velocity(m/s)

Reynolds Number Type of Flow Development Length (m)

1 1.058 2610.65 Laminar (Transitional) 2.877

2 1.527 3767.92 Turbulent (Transitional) 0.3298

3 1.764 4352.73 Turbulent 0.3378Table 7: Average velocity, Reynolds Number, flow type and

development length for Test 1, 2 and 3.

Reynolds Number can be calculated by using Equation 1 for each test.

Test 1: Test 2: Test 3:

ℜ=V Dv

ℜ=V Dv

ℜ=V Dv

= 1.058 x 0.019

7.7 x 10−6 = 1.527x 0.0197.7 x 10−6 = 1.764 x0.019

7.7x 10−6

= 2610.65 = 3767.92 = 4352.73

Development length is determined from Equation 8 and 9 for each test.

Test 1 (laminar): Test 2 (turbulent): Test 3 (turbulent):

¿D

=0.058ℜ ¿D

=4.4 (ℜ)16 ¿

D=4.4 (ℜ)

16

pg. 17

¿0.019

=0.058(2610.65) ¿0.019

=4.4 (3767.92)1 /6 ¿0.019

=4.4 (4352.73)1 /6

= 2.877m = 0.3298m = 0.3378m

Test 1 Test 2 Test 3

151.42D 17.36D 17.78D

Table 8: Development length in terms of D

As seen from Table 7, when the Reynolds number is low (laminar flow), the development

length is much higher than of a high Reynolds number (turbulent flow). Other than that, it

shown that laminar flow for test 1 and 2 while test 3 is determined as turbulent flow. Besides,

the transitional regimes between laminar and turbulent and Reynolds number is the only

parameter that affects the entrance length is shown in Table 7 in this experiment. The

velocity of fluid in the stream at a point can be regarded as time average of fluid velocity

which also is defined as mean velocity or average velocity. When the average velocity

increases, the Reynolds number also increases. From Table 8, the development length of test

1 is approximately ten times longer than development length for test 2 and 3 which are

shorter compared test 1. This is due to viscous effects are dominant within the boundary layer

in laminar flow. The viscous effects are negligible inviscid core. The thickness is growing

when moving down the downstream as it is dynamic phemomenon. From Figure 6, it is seen

that the boundary layer from the walls grows to such an extent they all merge on the

centreline of pipe. The flow is all viscous after inviscid core terminates and it said to be fully

developed. Thus, the length required for a fully-developed flow of laminar flow is longer than

turbulent flow.

pg. 18

Figure 6: Inviscid core and boundary layer of entrance length (Entrance length 2005)

4.3 Friction FactorFriction factor can be calculated by using Darcy-Weisbach equation while head loss is

determined from Bernoulli’s equation. The friction factors, f for each test (test 1 to 4) is calculated and tabulated as table shown below.

Table 9: Static head, head loss and friction factors for test 1 to 4

Calculated friction factors will be compared with the plotted values in Moody chart as shown

in Figure 7. By determining the friction factor, the Reynolds number can be estimated from

Moody chart as well. Below shows a table with the comparison made between theoretical

Reynolds number and experimental Reynolds number.

Test no Experimental friction factor

Reynolds from Moody chart

Theoretical Reynolds number

Theoretical friction factor

Test 1 0.0353 ~2000 2610.65 0.032Test 2 0.0360 ~5200 3767.92 0.0372Test 3 0.0362 ~5200 4352.73 0.0372Test 4 0.0264 ~2500 3195.45 -

Table 10: Experimental and theoretical friction factor and Reynolds number

The theoretical friction factor also is calculated to compare with the experimental factor. The

calculated theoretical factor is shown in Table 10 and details calculations of theoretical

friction factor can be referred to Appendix III.

From Table 10, there is huge difference is observed between the theoretical and experimental

Reynolds number. This may due to one of the reasons which is some of the flows are

transitional flow where the Reynolds number cannot be determined from Moody chart.

Experimental error like fluctuation due to occurrence of bubbles in flow speed also influence

the experimental friction factor to be different with theoretical friction factor. Another reason

is minor loses is negligible in the experiment, thus difference in head loss values may lead to

difference in experimental friction factor. Instrument error due to inconsistency of values

displayed by the machine when taking the readings of the static head also may lead to the

pg. 19

Test no.

Static Head, H (m) Head Loss,hL

(m) Friction factor, 𝑓Channel 1, H1 Channel 17, H2

Test 1 0.7030 0.3030 0.4 0.0353Test 2 1.236 0.3879 0.8481 0.0360Test 3 1.551 0.4121 1.139 0.0362Test 4 0.7394 0.2909 0.4485 0.0264

difference of the results. There is slightly different between the experimental and theoretical

friction factors as resulted from previous Reynolds number data.

Figure 7: Moody chart (Dr Hong Wei 2006)

pg. 20

4.4 Velocity Profile Velocity profile from experimental data can be calculated using formula,

V=√2 g∆ H . The linear relationship is well described shown by the formula itself. When the

dynamic head of the fluid increases, the velocity increases also. The calculated velocity

profile and dynamic head fluid from experimental data are tabulated as shown in Table 11

and 12 respectively

Distance from wall (mm)

ΔH (m)

Test 1 Test 2 Test 3 Test 4

1.0 0.07273 0.1576 0.1939 0.1455

3.0 0.1455 0.1939 0.2303 0.2545

5.0 0.2182 0.2424 0.2667 0.2909

7.0 0.2182 0.2667 0.2909 0.3151

8.5 0.2182 0.2424 0.2909 0.3030

9.5 0.1939 0.2424 0.2788 0.2909

Table 11: ΔH for test 1 to 4

Radius, r (m)Velocity (m/s)

Test 1 Test 2 Test 3 Test 4

0.0085 1.195 1.758 1.950 1.690

0.0065 1.690 1.950 2.126 2.235

0.0045 2.069 2.181 2.288 2.389

0.0025 2.069 2.288 2.389 2.486

0.0010 2.069 2.181 2.389 2.438

0.0000 1.950 2.181 2.339 2.389

Table 12: Radius and velocity of each radius point for test 1 to 4

Note: Details calculations for calculated values shown in Table 11 and 12 can be referred to Appendix IV.

pg. 21

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6

-0.01

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

0.01

Graph of Radius(m) Versus Velocity Profile(m/s)

Test 1 Test 2 Test 3 Test 4

Velocity (m/s)

Radi

us (m

)

Figure 8: Graph of radius versus velocity profile

1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.60

0.05

0.1

0.15

0.2

0.25

0.3

0.35

∆H(m) Against Velocity Profile(m/s)

Test 1Test 2Test 3Test 4

Velocity(m/s)

∆H(m

)

Figure 9: Graph of ΔH (m) against velocity profile(m/s)

pg. 22

The data from Table 11 and 12 is used to plot the distance from centre against

velocity profile graph as shown in Figure 8. Negative distances from centre are plotted where

the values of velocity profile are similar to the positive distances from centre. The velocity

profile shown in Figure 8 for test 1 is a parabolic shape which indicates that it is laminar

flow. Although the shape is not a fully-developed of parabolic shape, it is considered as

laminar flow due to low Reynolds number by judging Reynolds number obtained from

Moody Chart. The non-fully developed parabolic shape may due to the fluctuations happen in

flow speed of fluid as some turbulent effects spotted.

For test 2 and 3, by determining from Reynolds number obtained from Moody chart,

they are considered to be turbulent flow event though the turbulent flow velocity profile

shape characteristics is more clearly can be seen from test 2 than test 3. For test 4, it is in

transitional flow due to a bit irregular shape characteristics is shown. From the Reynolds

number which obtained from Moody chart, it is proved that it has to be transitional flow as its

Reynolds number falls in between the range of transitional flow.

Figure 9 shows that the linear relationship between the dynamic head of fluid and

velocity of fluid. When the velocity increases, the dynamic head of fluid also increases. An

almost linear straight line is plotted due to the very slightly difference between them. All

points lie in a straight line due to the numerous repeated constant numbers can be found as

shown in both tables whether based on distances either from walls or centres. This lead to the

mostly parabolic shape characteristics is clearly to be seen in some tests as the flow speed is

quite uniform and less steady effects are found. This may affect how to determine the type of

flow based on velocity profile shape and needed be compared with Reynolds number

obtained from Moody chart.

pg. 23

4.5 Discharge calculation method

Discharge is the product of the average velocity and cross sectional area. Cross

sectional area of the pipe can be determined depends on the geometric formula. Average

velocity can be determined by using the velocity profile of the fluid. The velocity increases

towards the centre of a tube under the conditions of laminar flow in a viscous fluid. Hence,

the average velocity for laminar flow can be calculated by divide the maximum velocity of

the fluid which located at the centreline of the pipe. However, for transitional flow and

turbulent flow, the maximum velocity of the fluid is hard to be identified. Another way to

find the average velocity is to total up the all velocities recorded at different radius and then

divided it with the number of velocity recorded. To reduce the error to find out the average

velocity, it is suggested to increase the number of velocity recorded to increase the accuracy

of result. Below shows the formulas can be used to calculate the discharge by using velocity

profile.

Average Velocity v=∑ vN

Discharge d=v ×π r2

pg. 24

4.6 Assessment of Error

There are several errors in this experiment. The first error is instrument error. The

pressure values that recorded are taken from a machine that displays the values in digital way.

The unstable values that shown by the machine during taking the readings is greatly affected

the accuracy of result as it gives difficulties to take a correct reading. Other than that, the

pressure value shown by the meter takes few minutes before the values come to stable, this

may due to the fluctuations occurred in flow speed of fluid as bubbles present. Moreover,

while waiting the value to become stable and consistent, this may cause the minor loses

energy in the pipe that which are not considered in this experiment. Parallax error when

measuring the discharge due to fluctuations occurred that causes values keep changing is

another error. Parallax error also occurs when adjusting the rod readings also can lead to

inaccuracy of the result. Diameter is considered consistent throughout experiment. The

inconsistent of diameter can affect the pressure drop and will affect the friction factor as well.

The friction factor varying with Reynolds number in this experiment is limited since it is only

to determine the laminar and turbulent flow and not valid for transitional flow.

5.0 Conclusion

All the Reynolds number is determined of each test for flow in a pipe with a circular

cross-section. The Reynolds number falls lower than 2100 is considered as laminar flow

while more than 4000 is considered as turbulent flow and between the range of these flows is

known as transitional flow which can be in either laminar or turbulent flow. The friction

factor concept in pipe flow was studied and investigated in this experiment. The fully-

developed flow friction factor was obtained to determine the Reynolds number from Moody

chart which also is used to determine type flow of each test was identified as well but it is

only valid for laminar and turbulent flow. The velocity profile was measured and compared

in both laminar and turbulent flows. The parabolic shape velocity profile is considered as

laminar flow while a more irregular shape velocity profile is considered as turbulent flow.

pg. 25

6.0 References

Dr. HongWei Wu, 2006. “Lecture 6: Viscous Flow in Pipe.” http://moodle.curtin.edu.my/pluginfile.php/14134/mod_folder/content/0/FM_230_Chap6.pdf?forcedownload=1.

Entrance Length. 2005. Aerospace, Mechanical and Mechatronic Engineering. http://wwwmdp.eng.cam.ac.uk/web/library/enginfo/aerothermal_dvd_only/aero/fprops/pipeflow/node9.html.

Head Loss Due To Friction In Circular Pipe. 2014. Accessed May 26,

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0CC4QFjAA&url=http%3A%2F%2Fwww.heacademy.ac.uk%2Fassets%2Fdocuments%2Fsubjects%2Fengineering%2Fcase-study-teaching-material-headloss-friction.doc&ei=bUGRU97SMI_h8AX7moLICA&usg=AFQjCNH27RPZe2mqrDJ9CeJ46KD1c7vEVQ.

Laminar and Turbulent flows in pipes. 2014. Accessed May 27, http://www.cs.cdu.edu.au/homepages/jmitroy/eng247/sect09.pdf.

Sleigh, Dr Andrew. 2009. Unit 4: Boundary Effects.

http://www.efm.leeds.ac.uk/CIVE/FluidsLevel1/Unit04/T2.html.

Types of flow. 2014. Alicat Scientific, Inc. Accessed May 25, http://www.alicat.com/technical-information/flow-principles/.

Viscous Flow In Pipes. 2014. Accessed May 25, http://civil.emu.edu.tr/old_website/data/civl332/chap3%20_revised.pdf.

pg. 26

7.0 Appendices

Appendix I

Table 2Discharge (Test 1):

The volumetric flow rate of 18L/min can be converted into SI unit m3

s.

18liter1min

× 1min60 s

× 0.001m3

1liter=3.00×10−4m3/s

Same method is applied on Test 2, Test 3, Test 4 and also for Test 5&6 respectively.

Average velocity (Test 1):

Average velocity can be determined from volumetric flow rate equation.

A=π D2

4=π (0.019 )2

4=2.835×10−4m2

V=QA

=(3.00×10−4 )

(2.835×10−4 )=1.058 m

s

Same method is applied on Test 2, Test 3, Test 4 and also for Test 5&6 respectively.

Table 5 and 6Piezometer head (Test 1):

Pressure, P in unit bar which obtained from experiment is converted into head form in unit m.

For Manometer No 1 where P is 0.058bar, head form is calculated as below.

P=0.058×̄ 100000Pa1 ¿̄=4800Pa ¿

H= Pρg

= 5800841×9.81

=0.7030m

This step is repeated for all manometers (manometer no. 1 to 19) and all tests (test 1 to 6).

The calculated results are tabulated and recorded in Table 5 and 6.

pg. 27

Appendix II

Table 9

Head loss, hL is calculated using Bernoulli’s equation.

¿ Equation5 :P1

ρg+V 1

2

2 g+z1=

P2

ρg+V 2

2

2g+z2+hL

hL=P1−P2

ρg+V 1

2−V 22

2g+z1−z2

SinceV 12=V 2

2∧z1= z2

hL=P1−P2

ρg=H1−H 2

¿ (0.7030−0.3030 )=0.4m

Each test (test 1to 4 )is calculated using same method and the answer obtained is substituted

to the Darcy-Weisbach equation to determine the friction factors, f for each test.

After that, substitute hL=0.4, L= 3.93-0.16=3.77 , V=1.058, D=0.019m, g=9.81(constant) and

friction factor of test 1 is obtained as shown below.

f=hLDL

2 gV 2

=0.4 ( 0.0193.77

2(9.81)1.0582 )

= 0.035m

All the results are tabulated in Table 9.

pg. 28

Appendix III

Table 10Theoretical friction factor is calculated as shown below.

For laminar flow,

f=64ℜ

For turbulent flow,

f=0.316

ℜ14

(Blasius formula)

For Test 1,

Test 1 is laminar flow, f= 64ℜ

= 64

2000

= 0.032

Test 2 is turbulent,

ƒ = 0.316 (Re)-0.25

= 0.316 (5200)-0.25

= 0.0372

For Test 3,

Test 3 is turbulent,

ƒ = 0.316 (Re)-0.25

= 0.316 (5200)-0.25

= 0.0372

All the results are tabulated in Table 10.

pg. 29

pg. 30

Appendix IV

The velocity for different distance from the wall or center is calculated using formula,

V=√2 g∆ H while the dynamic head,∆ H is actually the different between TP1 and TP2 in

head form shown in Table 3 and 4.

Table 11

Calculation for test 1 with the distance 1.0 mm from wall is as shown below:

∆H=TP 1−TP 2ρg

¿

¿ 0.033−0.027841×9.81

×100000

¿0.07273m

Same method is applied in each test 1 until 4 to determine the dynamic head in each test.

Table 12For first set distance from wall, 0.001m,

To obtain the radius of the pipe,

Radius=Diameter−2×distance¿wall ¿2

= 0.019−(2x 0.001)

2

= 0.0085m

Same method is applied for another five sets of distance from wall, 0.003m, 0.005m, 0.007m,

0.0085m and 0.0095m.

Velocity profile

For test 1,

V=√2 g∆ H

√2x 9.81 x0.07273

= 1.195 m/s

pg. 31

Same method is applied for the test 2 to 4.

pg. 32