Fluid Dynamics: Flow in Closed Conduits

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Chapter 11 Flow in Closed Conduits

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Main Topics

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Reynolds' Experiment Dimensional Analysis of Conduit Flow Friction Factor for Fully Developed Laminar Flow Friction Factor for Fully Developed Turbulent Flow Smooth Pipe Law Rough Pipe Law Different Workers Results Application    Energy/ pressure loss problem Velocity/ flow rate problem Pipe Sizing Problem

Explicit Equation for Friction Factor

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Main Topics
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Equivalent Diameter for Non- Circular Conduit Pressure Drop due to Fittings Loss of Head at Abrupt Enlargement Exit Loss Loss of Head at abrupt Contraction Entry Loss

Combinations of Pipes

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11.0 Introduction
In this chapter, we will go back to consider what we have left out in Chapter 7- viscous work done term. Because of this, this chapter is quite important for it is dealing with real practical problems. For chemical engineers, more than 90% of their problems involve flows in closed conduits.

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11.1 Reynolds' Experiment
The classic Reynolds experiment on viscous flow was conducted in 1883. Water is made to flow through a glass pipe as shown in Fig.11.1.1, the velocity being controlled by an outlet valve. At the inlet of the pipe, a dye having the same specific weight as water is injected into the flow. When the outlet valve is only slightly open, the dye will move through the glass pipe intact, forming a thread as illustrated in Fig.11.1.2.a. The orderly nature of this flow is apparent from this demonstration. However, as the valve is progressively opened, a condition will be reached whereby the dye assumes a fluctuating motion as it proceeds through the pipe. (As depicted in Fig.11.1.2.b.) A transition is taking place from the previous well ordered flow, which may be considered as laminar flow, to an unstable type of flow. Further opening of the valve then results in a condition whereby irregular fluctuations are developed in the flow so that the thread of dye is completely dispersed before proceeding very far along the pipe. (As shown in Fig.11.1.2.c.) This irregular flow is called turbulent flow. The experiment brings out the essential difference between laminar and turbulent flow. The former, while having irregular molecular motions, is macroscopically a well ordered flow. However, in the case of turbulent flow, there is the effect of a small but macroscopic fluctuating velocity superimposed on a well ordered flow. Visualization CN2122 / CN2122E

Figure 11.1.1 Reynold’s apparatus

11.1 Reynolds' Experiment
It was found by Reynolds that the criterion for the transition from laminar to turbulent flow in a pipe is the Reynolds number based on the pipe diameter. In the experiment, the Re was continuously increased by increasing the velocity. However, this could have been accomplished by using pipes of different diameters or using fluids with different viscosities or densities. A Re of approximately 2300 was found to denote the imminence of a transition from laminar to turbulent flow. Under special operating condition, it is found that laminar flow can be maintained for Re up to 40000. All experiments thus far indicated by most workers that below 2300, there can be only laminar flow. (However, Bird et al gives a value of 2100, to be on a safer side, we will take 2100 as the criterion.) Thus after 2100 has been reached, there may be a transition depending on the extent of local disturbances. We called this value (2100) of Re the critical Re.

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11.2 Dimensional Analysis of Conduit Flow
To consider the flow of fluid in a straight and horizontal circular pipe of constant cross section, we do not have to worry about the surface tension, because there is no free surface; there is no need to consider gravity, because the pipe is placed on an horizontal plane. We only have to consider the diameter of the pipe (D), the velocity of the...
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