Fluid Mechanics 230 Lab 2 Report(Yj)

Fluid Mechanics 230 Laboratory 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

Contents 1.0 Introduction ..................................................................................................................................... 3 1.1 Theory .............................................................................................................................................. 6 2.0 Experimental Procedure ................................................................................................................ 11 2.1 Apparatus used .............................................................................................................................. 11 2.2 Procedure....................................................................................................................................... 12 3.0 Results ............................................................................................................................................ 13 4.0 Analysis and Discussion.................................................................................................................. 16 4.1 Piezometer head ............................................................................................................................ 16 4.2 Development length ...................................................................................................................... 17 4.3 Friction Factor ................................................................................................................................ 19 4.4 Velocity Profile ............................................................................................................................... 21 4.5 Discharge calculation method ....................................................................................................... 24 4.6 Assessment of Error ....................................................................................................................... 25 5.0 Conclusion ...................................................................................................................................... 25 6.0 References ..................................................................................................................................... 26 7.0 Appendices..................................................................................................................................... 27

pg. 2

List of Tables Table 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 Figures Figure 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 (Types of flow 2014)

Figure 2 (b): Transitional flow

Figure2(c):Turbulent flow

(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. ̅

where

̅

Equation 1

= density of fluid ; ̅ = average velocity in pipe; D= diameter of pipe; = dynamic viscosity of fluid; = 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. √ where

Equation 2

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. ̅

Equation 3

̅

where

Equation 4

=head loss due to friction; f = friction factor; L= Pipe length (distance between two piezometer points); D= Internal diameter pipe; ̅ = Average flow velocity; g = gravitational acceleration; =dynamic viscosity; = density

In this experiment, head loss,

can be calculated by using Bernoulli’s equation as shown as

formula below.

̅

̅

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 ̅

̅

, 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