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CLOSED CONDUIT FLOW

“The wisest mind has something yet to learn.” George Santayana

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“The first great gift a teacher can bestow on his student is a good lab manual.”

Fluid Mechanics for Civil Engineering II

CLOSED CONDUIT FLOW ACKNOWLEDGMENT

We would like to thank all who helped and encouraged us to complete this laboratory manual; especially, our fluid mechanics professor, Prof. Cornelio Dizon for guiding us throughout our research work.

Also, special thanks to Kuya Cesar, Cesar Catibayan, who has guided us very well in handling the instruments used in this manual.

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Alvin Seria Imee Bren Villalba Jannebelle Dellosa Jaime Angelo Victor

Fluid Mechanics for Civil Engineering II

CLOSED CONDUIT FLOW TABLE OF CONTENTS

Page Introduction …………………………………………………………………………………………………..

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Oil Pipe Assembly Experiment 1: Laminar and Turbulent Flow ……………………………………….

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Air Pipe Assembly Experiment 2: Smooth and Rough Pipes …………………………………………….

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Water Pipe Assembly Experiment 3: Minor Losses ……………………………………………………………….

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Hydraulic Bench ................................................................................................

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Experiment 4: Calibrating a Venturi Meter …………………………………………

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Experiment 5: Calibrating a Flow Nozzle …………………………………………….

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Experiment 6: Calibrating an Orifice Meter ………………………………………..

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References …………………………………………………………………………………………………….

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Appendix A: …………………………………………………………………………………………………….

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Derivation of Bernoulli’s Equation Derivation of V-notch weir discharge equation Appendix B …………………………………………………………………………………………………….

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Life and Works of Bernoulli Life and Works of Froude

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Life and Works of Reynolds

Fluid Mechanics for Civil Engineering II

CLOSED CONDUIT FLOW INTRODUCTION

There are two main classes of flow in fluid mechanics. The flow of fluids around bodies such as airfoils, rockets, and marine vessels is called external flow. This becomes the case when the other boundaries of the flow are comparatively distant from the body. One general type of this flow is open channel flow, also called free surface flow, wherein the fluid stream has a free surface exposed to atmospheric pressure, and gravity is the only component acting along the channel slope. This type of flow is encountered in natural bodies of water such as rivers, streams, and oceans, as well as in man-made hydraulic structures such as floodways, dams, and canals. On the other hand, flows that are enclosed by boundaries are termed internal flows. Examples of this type of flow include the flow through pipes, ducts, and nozzles.

This research paper focuses primarily on the latter class of flow, that is, the flow of fluids in closed conduits such as pipes. Different topics under this type of flow were discussed in detail. These topics include laminar and turbulent flow, circular and non-circular conduits, smooth and rough pipes, major and minor losses in pipes, single-pipe flow problems, series and parallel pipes, and branching pipes. Moreover, much attention is given to the detailed discussion of the different experimental apparatuses used in the study of flow in pressure conduits. Such apparatuses include the oil pipe ass embly, air pipe assembly, water pipe assembly, water tunnel, and hydraulic bench. Finally, different experiments that

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can be conducted using these facilities were also discussed thoroughly.

Fluid Mechanics for Civil Engineering II

CLOSED CONDUIT FLOW INTRODUCTION

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Pipes are the most common tools used in the analysis of closed conduit flow. Usually, pipes used in engineering practice are long hollow cylinders; however, cross sections of a different geometry are used occasionally. Pipes can be smooth or rough, depending on the type of material from which they were constructed. There are commercially available pipes made of cast iron, galvanized iron, commercial steel, brass, lead, copper, glass, smooth plastic, and concrete, to name a few.

Figure 1. Type of commercial pipes

Fluid Mechanics for Civil Engineering II

CLOSED CONDUIT FLOW INTRODUCTION

Moreover, the pipe system will not be complete without pipe fittings. Pipe fittings or connections are used to join different pipes, such as, bends, junctions, tees, etc. They are also used to control or alter the flow of the fluid through the pipe, this includes valves, gradual contraction and expansion, sudden contraction and expansion, bell-mouthed entrance and more others.

Laminar and Turbulent In 1883, Osborne Reynolds conducted an experiment on viscous flow. The results of his investigation showed that there are two distinct types of fluid flow, namely, laminar flow and turbulent flow. In his experiment, he allowed water to flow from a large tank to a long glass tubing (see Figure 1). An outlet valve was placed at the end of the tube to allow him to have complete control over the fluid velocity by varying the discharge out of the tube. At the entrance, he injected a very thin stream of colored liquid having the same density (or specific weight) as the water in the tank.

a.) Laminar Flow

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Figure 2. Reynolds Experiment

Fluid Mechanics for Civil Engineering II

CLOSED CONDUIT FLOW INTRODUCTION

With the outlet valve only slightly opened, that is, when the velocity of the liquid in the tube is small, he observed that the colored liquid moved in a straight line as illustrated in Figure 2a. As the valve was progressively opened, the velocity of the liquid in the tube gradually increased, and a fluctuating motion of the colored fluid was observed as it moved through the length of the tube (Figure 2b). Finally, when the valve was further opened, it was observed that the colored liquid is already completely dispersed at a short distance from the entrance of the tube such that no streamlines could be distinguished (Figure 2c). The type of flow illustrated in Figure 2a is known as laminar flow, also called streamline flow. Reynolds described it as a well-ordered pattern whereby fluid layers are assumed to slide over one another.. Figure 2b shows a transition flow from the previous laminar flow to an unstable type of flow. Finally, Figure 2c demonstrates a completely irregular flow called turbulent flow.

c.) Turbulent Flow

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b.) Transition Flow

Fluid Mechanics for Civil Engineering II

CLOSED CONDUIT FLOW INTRODUCTION

Energy Losses Fluid in motion offers frictional resistance to flow; wherein some part of the energy of the system is converted into thermal energy (heat). In fluid mechanics this converted energy is referred as “energy loss” or “head loss”. This energy loss is due to fluid friction as well as to valves and fittings. The former is more known as major losses; while, the latter as minor losses. The energy loss in long pipelines, with length to diameter ratio exceeding 2000, is mainly due to major losses, while minor losses are negligible. Otherwise, minor losses are dominant over minor losses in short pipelines.

Major Losses These are the energy dissipated through the walls of the pipe in which the fluid is flowing. Moreover, the magnitude of the energy loss is dependent on the properties of the fluid, the flow velocity, the pipe size, and smoothness of the pipe wall, and the length of the pipe.

Rough and Smooth Pipes As mentioned, major losses are dependent on the smoothness of the pipe wall. Pipe walls can either be rough or smooth depending on its material composition. For example a galvanized iron pipe is a type of a smooth walled pipe; while, a brass pipe is a rough walled pipe.

Minor Losses

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Elements that control the direction or flow rate of a fluid in a system typically set up local turbulence in the fluid, causing energy to be dissipated as heat. Whenever, there is a restriction, a change in flow velocity, or a change in the direction of flow, these energy losses occur. Moreover, in large systems the magnitude of losses due to valves and fittings is usually small compared to frictional losses; hence, they are referred as minor losses.

Fluid Mechanics for Civil Engineering II

CLOSED CONDUIT FLOW EXPERIMENTS Laminar and Turbulent Flow

Objective: 1.) 2.) 3.) 4.)

To determine the range of Reynolds number for laminar, transition and turbulent flow. To verify that the friction loss in laminar flow is equivalent to 64/Re. To verify the Hagen-Poiseuille equation. To determine the measurement uncertainties, and compare the results with benchmark data.

Introduction: Energy losses in closed conduits are classified into major and minor losses. Major losses result from the resistance of the conduit walls to the flow and minor losses are due to pipe appurtenances that cause a change in the magnitude and/or direction of the flow velocity. The determination of these losses is important for the specification of a pipeline design. Head losses mainly results from internal pipe friction when the ratio of the length of a pipeline to its diameter exceeds 2000 and minor pipe appurtenances are not present in a pipe. In this experiment, major losses are calculated and minor losses are assumed negligible. Theoretical background: The head loss for a pipe system is determined by the energy equation between two sections of the pipe given by P1/γ + Z1 + V12/2g = P2/γ + Z2 + V22/2g + HL

(1)

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Where P is the pressure at the centreline of the pipe, γ is the specific weight of the fluid, Z is the elevation of the centreline of the pipe relative to an arbitrary datum, V is the average flow velocity, g is the gravitational constant and H L is the total energy loss between section 1 and 2. When minor losses are negligible, HL is mainly due to frictional losses only.

Fluid Mechanics for Civil Engineering II

CLOSED CONDUIT FLOW EXPERIMENTS Laminar and Turbulent Flow

The velocity is determined when the discharge is known, using the equation Q = AV

(2)

Where Q is the discharge, A is the area of the pipe, and V is the velocity in the pipe. If the pressures at section 1 and 2 are known, the energy equation can be used to determine the head loss along the pipe. The pipe head loss due to friction is obtained using the Darcy-Weisbach equation: f = HL LV2 / 2Dg

(3)

Where f is the friction factor, L is the length of the pipe section, and D is the pipe diameter. The Moody diagram shows the relationship between the friction factor, relative roughness of the pipe and Reynolds Number. There are three zones of flow in the diagram, namely, laminar, transition and turbulent. Type of flow Laminar Transition Turbulent

Reynolds Number Re