Head Loss in Pipe Flow ME 123: Mechanical Engineering Laboratory II: Fluids


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1 Head Loss in Pipe Flow ME 123: Mechanical Engineering Laboratory II: Fluids Dr. J. M. Meyers Dr. D. G. Fletcher Dr. Y. Dubief
2 1. Introduction Last lab you investigated flow loss in a pipe due to the roughness of the pipe s walls. Losses will also occur with the introduction of various components in fittings within the pipe system. The losses due to these fittings are strongly dependent on geometry, coupling methods between elements, and internal roughness. These loses are classified as minor losses but when enough components are added to a pipe system appreciable flow loss can be encountered. When designing a flow system where the knowledge of flow rates is important it is imperative that the design of said system includes an analysis of all potential loss mechanisms. In this lab you will learn how to determine the loss, which is normally called the head loss, of various components in the same pipe flow facility you used in the last lab. Unlike losses caused by friction, minor losses can be assumed independent of Reynold s number in turbulent flows (see Chapter 6 of White, Fluid Mechanics). Lab Objectives: Experimentally understand head loss analysis To understand how various tube fittings impact pipe flow loss Understand how head loss can be used to meter flow rates 2. Experimental Arrangement The pipe flow facility (Figure 1) has been modified to accommodate the 90 turns of the tube fittings. Recall the straight tube section has an internal diameter of 80 mm and is fitted with 11 access ports that provide an entry for Pitot measurements or can be fitted with a static pressure tap. Locations each tap and Pitot port is listed in Table 1. Bear in mind that the distance values beyond will change once a fitting is installed. A blower on the left side of the facility pulls air through the tube (flow is from right to left). A manometer is attached to the facility and is used to monitor atmospheric, Pitot, and static pressure levels. Note that the manometer bank can be tilted to increase pressure sensitivity, which can be useful for the Pitot pressure surveys. For these measurements the tilted angle influences the dynamic pressure as: 2 = h h cos (1) where is the density of air, h is the height of the manometer for the Pitot measurement, h is the height of the manometer for the static pressure measurement at the Pitot survey location, and is the manometer bank angle w.r.t. vertical. The manometer working fluid is a kerosene base with density of =787 kg/m 3. Be sure to write (in your own words!) a concise, yet sufficiently detailed, explanation of how the different components of the experiment work as this information will be used to describe your experiment in your report.
3 Figure 1: Pipe experiment Table 1: Locations of Pitot and static pressure tap stations 3. Measurements Each group will get about 20 to 30 minutes to perform measurements and afterward, if time allows after, groups needing/wanting more time may continue with measurements. The lab is always available outside of scheduled lab times if sufficient measurements cannot be performed in the allotted time. Refer to last lab handout (Turbulent Velocity Profile Development in a Pipe) for details on resolving Pitot measurements into velocities. For each measurement record your respective error in a column/space just to the right as ±. 3.1 Inlet Velocity Profile You are required to take a velocity profile at the inlet of the tube. This is required to determine your average velocity of the flow. Measure,, and at each measurement point with the Pitot probe (see Figure 2) just like last lab. Measure first these values at the centerline ( = 38.5 mm). Move the Pitot probe to the bottom surface ( = 0 mm) and measure again. Move up in 2.5 mm increments until you see a constant profile which should only be a few steps (give or take). At this point assume the velocity is constant and move to the next step of measurements.
4 Figure 2: Translating Pitot probe mm radius Elbow Losses A flanged 80 mm inside diameter 90 elbow (Figure 3) is to be inserted between station 6 and 7. Static pressure will be recorded upstream and downstream of this fitting. The bulk velocity acquired from your inlet velocity profile survey will be used as your average velocity,. With the pressure drop and average velocity value you will determine the head loss, h, and resistance coefficient,, for this fitting from Equations 5 and 6. For this measurement, you only need to take the static pressure before and after. Figure mm radius 90 bend 3.3 Mitered Elbow with Turning Vanes Remove the 200 mm elbow between stations 6 and 7 and replace with the mitered elbow (Figure 4). Static pressure will be recorded upstream and downstream of this fitting. The bulk velocity acquired from your inlet velocity profile survey will be used as your average velocity,. Again, with the pressure drop and average velocity value you will determine the head loss, h, and the resistance coefficient,, for this fitting from Equations 5 and 6.
5 Figure 4: 90 mitered elbow with turning vanes 3.4 Orifice Plate Restriction Meter The pipe flow orifice is one of a family of restriction meters which uses a pressure drop to measure flow rate. Remove the elbow and place the orifice between Station 6 and Station 7. Measure the pressure just upstream and downstream of this insert. Recall that ultimately this is a device to determine mass flow from pressure drop measurements. But this requires a calibration that quantifies the degree of deviation from the ideal Bernoulli equation. This deviation is defined as and is commonly called the discharge coefficient and is discussed more in Section 4.5. Figure 5: Orifice restriction meter insert.
6 4. Reduction of Data 4.1 Bulk Velocity The bulk (average) velocity,, is the average pipe velocity that may be calculated based on a Pitottube inlet traverse and a ring wall static pressure reading at the pipe inlet accounting for the small boundary layer at the inlet station through the following relation: = 2!!! (2) Since the cross section area of the tube is constant, it follows that the average velocities are constant as well ( # = =). 4.2 Reynold s Number Reynold s number based on tube diameter, $, can be calculated using the average velocity through: Re ' = $ ( (7) Can you determine if the flow is laminar or turbulent? 4.3 Head Loss The energy equation, as derived/illustrated in class, between two cross sections of the pipe, can be written as: ) # * +, # # 2* + #. ) * +, 2* +.=h (3) Where,, and  are the pressure bulk/average velocity, and height respectively. The fluid density is and the magnitude of gravity is *. This gives a relation to determine the head loss, h, between sections 1 and 2. Keep in mind that head loss has units of length. With these simplifications it can be shown that the pressure drop measured between any two stations is equivalent to the head loss between them: # = =*h (4) 4.4 Head Loss Across a Fitting In class we defined a loss coefficient term,. This term can is related to the head loss through:
7 with: h = 2* (5) = 1 2 (6) The pressure difference = hcos * is taken between the pressure taps immediately upstream and downstream of the fitting. The density of air and manometer kerosene are denoted as and, respectively. The angle of the manometer bank with respect to the vertical is denoted as. 4.5 Restriction Meter Flow Rate Correction Factor The flow rate obtained by the modified Bernoulli equation for an orifice with flanged taps (to be derived in the report) is: 0=1 = where 0 is the volume flow rate, is the bulk velocity, is the variation of pressure across the orifice, is the density of the fluid, and 4 is the ratio of orifice diameter to pipe diameter. The orifice plate (see Figure 5) has a diameter of 50 mm and is also to be placed between stations 6 and 7 at ~1404 mm downstream from the inlet nozzle. The volume flow rate is to be determined from the bulk velocity flow and area cross section of the tube. Determine the discharge coefficient,, of the orifice with the above relation. Once the discharge coefficient is known, the expression in Equation 5 can be used to determine mass flow through a simple measurement of pressure drop using: 67 =0 (9) (8)
8 5. Analysis and Discussion for Report You are required to discuss the results based on the literature (compare with existing plots!!). You are also required to show all uncertainties. Show your measured entrance velocity profile and determine the average velocity for your head loss measurements. Determine tube diameterbased Reynolds number comment on whether the flow is laminar or turbulent. Your study of head loss for of the two bends and they should show uncertainties with nominal values compared to that of the literature. Perform a discharge coefficient analysis for the orifice. Calculate the mass flow through the orifice which ultimately gives you the constant mass flow through the tube. What is the sensitivity of this device? In other words, when you change mass flow by a certain amount, is there enough resolution in your pressure measurements to resolve this mass flow? Develop a velocity uncertainty equation derived from all measured parameters for both methods. Recall the general expression for uncertainty as explained in your notes: 8 9 =38 :; < =? +8 => < =? +8 # => :A < =? + +8 => :D < =? B => E (10) Determine which measured values affect the precision of your measurements the most (and least) using a measured parameter sensitivity analysis (described in Lecture 1).
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