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FSU EML 4304L - Experiment 5

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Experiment 5 Pipe Flow: Major and Minor Losses Objectives The goal of this laboratory is to study pressure losses due to viscous (frictional) effects in fluid flows through pipes. These pressure losses are a function of various geometric and flow parameters including pipe diameter, length, internal surface roughness and type of fitting. In this experiment, the influence of some these parameters on pressure losses in pipe flows will be evaluated by measuring flow rates through different types of pipes. Theoretical Background Head Loss in Pipe Flows Pipe flows belong to a broader class of flows, called internal flows, where the fluid is completely bounded by solid surfaces. In contrast, in external flows, such as flow over a flat plate or an airplane wing, only part of the flow is bounded by a solid surface. The term pipe flow is generally used to describe flow through round pipes, ducts, nozzles, sudden expansions and contractions, valves and other fittings. In this experiment we will limit our study to flow through round pipes and pipe fittings, such as elbows and valves. When a gas or a liquid flows through a pipe, there is a loss of pressure in the fluid, because energy is required to overcome the viscous or frictional forces exerted by the walls of the pipe on the moving fluid. In addition to the energy lost due to frictional forces, the flow also loses energy (or pressure) as it goes through fittings, such as valves, elbows, contractions and expansions. This loss in pressure is mainly due to the fact that flow separates locally as it moves through such fittings. The pressure loss in pipe flows is commonly referred to as head loss. The frictional losses are referred to as major losses (hl) while losses through fittings, etc, are called minor losses (hlm). Together they make up the total head losses (hlT) for pipe flows. Hence: hlT = hl +hlm (1) Head losses in pipe flows can be calculated by using a special form of the energy equation discussed in the next section. Energy Equation for Pipe Flows Consider steady, incompressible flow through a piping system. The energy equation between points 1 and 2 for this flow can be written as: lThgzVPgzVP222221211122 (2) In the above equation, the terms in the parenthesis represent the mechanical energy per unit mass at a particular cross-section in the pipe. Hence, the difference between the mechanical energy at two locations, i.e. the total head loss, is a result of the conversion of mechanical energy to thermal energy due to frictional effects.The significant parameters in equation 2 are described below: - z, is the elevation of the cross section, taken to be positive upwards. -  is called the kinetic energy factor. For laminar flow  = 2, for turbulent flow  = 1. - Flow in a pipe is considered laminar if Reynolds number, ReD < 2000, where ReD = VD/. - V is the average velocity at a cross section. - hlT, as discussed earlier, is the total head loss between cross-sections 1 and 2. Details of calculating the head loss are discussed in the next section. An examination of equation 2 reveals that for a fixed amount of mechanical energy available at station 1, a higher head loss will lead to lower mechanical energy at station 2. The lower mechanical energy can be manifested as a lower pressure, lower velocity (i.e. lower volumetric flow rate), a lower elevation or any combination of all three. It should also be noted that for flow without losses, hlT = 0 and the energy equation reduces to Bernoulli’s Equation. Calculation of Head Loss Major Losses The major head loss in pipe flows is given by equation 3. 22lLVhfD (3) where L and D are the length and diameter of the pipe, respectively, V is the average fluid velocity through the pipe and f is the friction factor for the section of the pipe. In general, the friction factor is a function of the Reynolds number and the non-dimensional surface roughness, e/D. The friction factor is determined experimentally and is usually published in graphical form as a function of Reynolds number and surface roughness. The friction factor plot, shown in Fig. 1,(attached) is usually referred to as the Moody Plot, after L. F. Moody who first published this data in this form. When the Reynolds number is below 2000 and the flow can be assumed to be laminar, the friction factor is only a function of the Reynolds number and is given as: DarlafRe64min (4) Minor Losses The minor head losses which for some cases, such as short pipes with multiple fittings, are actually a large percentage of the total head loss - hence, not really ‘minor’ - can be expressed as: 22VKhlm (5) where K is the Loss Coefficient and must be determined experimentally for each situation. Another common way to express minor head loss is in terms of frictional (major) head loss through an equivalent length, Le, of a straight pipe. In this form, the minor head loss is written as: 22VDLfhelm (6) Loss coefficients, K and equivalent lengths can be found in a variety of handbooks; representative data for limited fittings is available in most undergraduate Fluid Mechanics texts.The calculation of head loss for flow through a pipe with known conditions is generally carried out as follows. If the fluid velocity and the pipe diameter are known, the Reynolds number can be calculated. The Reynolds number and the pipe roughness are used to determine the friction factor, f, from the Moody plot using the appropriate curve. Once, the friction factor is known, the major head loss can be calculated from equation 3. The head loss can then be used to determine the pressure drop between two sections from equation 2. A reliable estimate of the pressure loss is critical for determining the hardware requirements, e.g. pump size, for a specific task. Conversely, if the head loss, i.e. the pressure drop due to frictional losses, is measured then the friction factor, f, can be calculated using the energy equation. This is the case in the present experiment; the pressure drop is measured for a range of flow rates corresponding to different Reynolds number, hence the friction factor can be calculated as a function of Reynolds number. These


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