Fluids, Lesson 9 (part II): Pipe Flow Minor Losses MECE-251 Fluids, Lesson 9 (part II): Pipe Flow Minor Losses 1 - Read Text Sections 2 - Solve Chapter Problems 3 & 4 – Lectures, Example, and Review Problems Hello again and welcome to the second lecture of Lesson 8. 5 - Solve Case Study 6 - Complete On-line Lesson Quiz R·I·T MECE-251 1

Objectives Discussion and calculation of “minor losses” In the last lecture, we discussed "major" losses. In this lecture, we'll discuss "minor" losses. R·I·T MECE-251 2

Energy Considerations in Pipe Flow Major Losses: Friction Factor Head Loss In the last lecture, we discusses losses due to friction along the walls of pipes and termed this “losses”. More specifically, this type of losses are called “major losses”. They are those that are caused by long lengths of straight pipe where the flow is fully developed. The net pressure loss from these is proportional to the length of pipe, which makes intuitive sense. The losses from two 10m pipes joined end to end will be two times the losses through one 10m pipe if the flow is fully developed. R·I·T MECE-251 3

At the same time, it’s clear that some other components in a system could cause us to lose pressure. For instance, the entrance region of a pipe or flow through the tortuous path of a valve that is partially or fully open. These losses act more as singularities as they are not proportional to the length of pipe, they occur at a nearly discrete location within the piping system. In general, they are caused by some sort of geometry that causes a flow disturbance so that the flow is no longer fully developed. The disturbed flow introduces additional shear stress and energy loss. Fundamentals of Fluid Mechanics, 5/E by Bruce Munson, Donald Young, and Theodore Okiishi Copyright © 2005 by John Wiley & Sons, Inc. All rights reserved.

Calculation of Head Loss Minor Loss: Loss Coefficient, K Minor Loss: Equivalent Length, Le Losses caused by this sort of singular flow disturbance, are known as "minor losses". They are not proportional to the length of pipe, they're just the result of the existence of the single object, be it a valve or elbow or contraction. For many items we can find a given value, K, the minor loss coefficient and calculate the head loss from this equation. Again, we see that the energy lost is proportional the kinetic energy of the flow, we're essentially losing a fixed portion of the kinetic energy. The minor loss coefficient would be determined by a table lookup and these exist for most common items. For some objects, an equivalent Length is used instead of K. If this equivalent length, Le, is given then we use the equation for major losses but with an equivalent length. This is sometimes convenient in that the equivalent length can be simply added to the actual length of pipe so that there is only one loss term – accounting for the major and minor losses. Lastly, I should make it very clear that the term "minor" should not imply that these are insubstantial or smaller in value that major losses. That actually depends on the piping system. In some systems, with many bends, valves, expansions relative to the length, the "minor" losses may truly dominate the total pressure loss. In other systems with long straight lengths of pipe and only a few fittings, major losses will likely dominate.

(c) slightly rounded, KL = 0.2. (d) well-rounded, KL = 0.04. (a) Reentrant, KL = 0.8. (b) sharp-edged, KL = 0.5. Losses are experienced for many different shapes, including entrances. We saw the reason for this earlier, including the growth of the boundary layers, but flow disturbance and separation may also contribute. Nonetheless, all of this is lumped into a single loss coefficient. The loss coefficient does depend on the exact geometry, but not the size of the pipe. Some more common ways that a pipe might be joined to a tank are shown here with the loss coefficients listed. Note that the smoother the geometry and flow the lower the losses. (c) slightly rounded, KL = 0.2. (d) well-rounded, KL = 0.04. Fundamentals of Fluid Mechanics, 5/E by Bruce Munson, Donald Young, and Theodore Okiishi Copyright © 2005 by John Wiley & Sons, Inc. All rights reserved.

This graph shows the same data, but with the K as a function of the curvature of the entrance as a continuous function. Fundamentals of Fluid Mechanics, 5/E by Bruce Munson, Donald Young, and Theodore Okiishi Copyright © 2005 by John Wiley & Sons, Inc. All rights reserved.

Here is a similar chart for a pipe reduction Here is a similar chart for a pipe reduction. Note that the chart is very specific in saying that the head loss should be calculated with using the velocity of the exit pipe, which has a higher velocity. This is critical as V2 could be very different from V1. Unfortunately, all charts do not use the downstream value – some use upstream, so you need to be careful when looking up a loss coefficient that you are using the correct velocity. Figure 8.26 (p. 440) Loss coefficient for a sudden contraction (Ref. 10). Fundamentals of Fluid Mechanics, 5/E by Bruce Munson, Donald Young, and Theodore Okiishi Copyright © 2005 by John Wiley & Sons, Inc. All rights reserved.

Here is similar data for a sudden expansion, here using the inlet velocity, which is still the higher velocity. Figure 8.27 (p. 441) Loss coefficient for a sudden expansion (Ref. 10). Fundamentals of Fluid Mechanics, 5/E by Bruce Munson, Donald Young, and Theodore Okiishi Copyright © 2005 by John Wiley & Sons, Inc. All rights reserved.

Figure 8.31 (p. 443) Character of the flow in a 90 mitered bend and the associated loss coefficient: (a) without guide vanes, (b) with guide vanes. Fundamentals of Fluid Mechanics, 5/E by Bruce Munson, Donald Young, and Theodore Okiishi Copyright © 2005 by John Wiley & Sons, Inc. All rights reserved.

Figure 8.30 (p. 443) Character of the flow in a 90 bend and the associated loss coefficient (Ref. 5). Fundamentals of Fluid Mechanics, 5/E by Bruce Munson, Donald Young, and Theodore Okiishi Copyright © 2005 by John Wiley & Sons, Inc. All rights reserved.

Table 8. 2 (p. 445) Loss Coefficients for Pipe Components (Data from Refs. 5, 10, 27) Fundamentals of Fluid Mechanics, 5/E by Bruce Munson, Donald Young, and Theodore Okiishi Copyright © 2005 by John Wiley & Sons, Inc. All rights reserved.

Approximate friction loss for PVC and CPVC fittings in Equivalent Length in feet of Straight Pipe for water can be found in the table below: The table can also used for other thermoplastic pipes materials with similar design. The values can be used to calculate pressure loss with the Equivalent Pipe Length Method. Friction Loss Equivalent Length - feet of Straight Pipe (ft) Fitting Nominal Pipe Size (inches) 1/2 3/4 1 1 1/4 1 1/2 2 2 1/2 3 4 6 8 10 12 90o Elbow, long sweep radius 1.5 2.0 2.5 3.8 4.0 5.7 6.9 7.9 12.0 18.0 22.0 26 32 90o Elbow, standard sharp inside radius 3.6 4.5 5.3 6.7 7.5 8.6   11.1 13.1 45o Elbow 0.8 1.1 1.4 1.8 2.1 2.6 3.1 5.1 8.0 10.6 13.5 15.5 Gatevalve 0.3 0.4 0.6 1.0 3.0 Tee Flow - Run 1.7 2.3 2.7 4.3 6.2 8.3 12.5 16.5 17.5 20.0 Tee Flow - Branch 5.0 6.0 7.0 15.0 16.0 32.7 49.0 57.0 67.0 Male/Female Adapter 2.8 3.5 5.5 6.5 9.0 14 From: http://www.engineeringtoolbox.com/pvc-pipes-equivalent-length-fittings-d_801.html

Next Steps L9 Task 4B: Please review the example problems on line. L9 Task 4C: Then, solve the review problem. L9 Task 5: Form groups and work on your case study. L9 Task 6: Take the Lesson 9 quiz. From the first part of this lecture, we can calculate some stresses in simple laminar viscous flows. The second part was largely conceptual, but we will begin to calculate losses in pipes in the next weeks. I wanted to make the connection between shear stress and pressure losses clear before we continued. Now, its time for me to solve an example problem, for you to attempt the review problem, and then to move finish the lesson. Reference: Schaum’s Outline of Thermodynamics for Engineers, Second Edition, M.C. Potter and C.W. Somerton, McGraw Hill Several Images are from Fundamentals of Fluid Mechanics, 5/E by Bruce Munson, Donald Young, and Theodore Okiishi R·I·T MECE-251 14