Group 6B
Minor losses in bends and fittings
By Alex Starrett C3200095 Due date: 11/4/16
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Aims: the aims of this experiment were to determine the dimensionless loss coefficient K for various bends and fittings, and compare them to published values.
Experimental: 1. Apparatus. The components of the apparatus are listed below. Hydraulics bench. Losses in bends and fittings pipe network. Stop watch on mobile phone. Pump. Picture of the hydraulics bench and pipe network are shown in figure 1.
F1-22 Armfield (2010). Figure 1: hydraulics bench and pipe network
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2. Procedure Engage the pump to bleed all the air from the line. By turning the flow control valve located at the right hand rear of the apparatus start increasing the flow rate. Make sure that the flow rate does not increase to the point were the menisci in the manometers go off the scale (at the top or the bottom of the manometer). The pipe network consists of a water inlet, long radius bend, a small radius bend, mitre, 90 elbow an enlargement and a contraction (a sketch of the enlargement/contraction is shown in figure 2). Take time to identify the direction of the flow and which manometers correspond to each bend/fitting. Take manometer readings for all the fittings and bends in the pipe network, h1 and h2. Drop the rubber ball to seal off the hole in the collection basin. Record the time taken to collect a measured quantity of water using a stopwatch and the tanks volume gauge. A greater accuracy is obtained by collecting a larger amount of water. Raise the rubber ball to let the collected water return to the system. Repeat this process 6 times making sure to decrease the flow rate each time by adjusting the flow control valve. D is the diameter of the pipe in (mm).
Figure 2: Sketch of the enlargement and contraction in the pipe network Results and discussion: There are two types of losses associated with bends and fittings in pipes. The shear stress between the water and the internal pipe surface is referred to as major loss. The energy loses due to the bends and fittings of a particular pipe network are called minor losses, together they determine the head loss of the system Potter, et al (2012). 3
Minor loses can be shown in terms of the loss coefficient K and is defined by:
H =
KV 2 2g
(1)
Where H is the water column height (mm), K is the dimensionless loss coefficient, V is velocity of the fluid (m/s) and g is the gravitational constant (m/s^2). The K value for each individual bend and fitting must be determined experimentally. For the bends in the system H can be taken as the difference between h1 and h2. The cross sectional area of the pipe and therefore the velocity does not change due to the conservation of mass equation. Q V1 A1 V2 A2
(2)
Where Q is the flow rate, V1 & V2 are velocities (m/s) in the respective areas of the pipe A1 & A2 in (m^2). For the Expansion and contraction shown in figure 2 the Bernoulli equation must be used to determine P1 & P2.
z1
2 1
(3)
2 2
V p V p 1 z2 2 hL 2g g 2g g
Where P1 & P2 are the liquid pressure between the pipe sections (m of water), is water density (kg/m^3), g is the gravitational constant (m/s^2), V1 & V2 are velocities at each point (m/s) and Z1 & Z2 are the relative elevations at each point (m). Note Z1 & Z2 are negligible for this experiment. Rearranging for head loss and using equation (2) we can use: hL
V V h h z z 2g 2 1
1
2
2 2
1
2
(4)
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The raw data collected during the experiment is shown in Appendix A. Sample calculations of the expansion/contraction pressure differences are contained in Appendix B.
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A graph showing the results of the experiment taken over 6 different flow rates is shown in figure 3. H vs V2/2g. 0.1 0.09
Delta H (m)
0.08
mitre
0.07
Linear (mitre)
0.06
Linear (elbow)
elbow short bend
0.05
Linear (short bend)
0.04
long bend
0.03
Linear (long bend)
0.02
enlargement Linear (enlargement)
0.01
contraction
0 0.01 0.02 0.03 0.04 0.05 0.06
Linear (contraction)
v^2/2g (m)
Figure 3 experimentally determined values of H and V2/2g. It can be noted from the graph in figure 3 that all results are trending towards the origin. From the graph it can also be shown that the tighter bends had greater losses when compared to the longer drawn out bends and the enlargement or contraction. When comparing the mean values of k with the published values as in Appendix E, the experimentally derived values are within the calculated error range for the mitre, elbow, short bend and the long bend. Error analysis is shown in Appendix C and the error for each bend is shown in Appendix D. The published K values for the expansion and contraction were not within the error range of the derived K values. The omission of z from Equation (4) may have contributed to this. Due to time management problems during the experiment the final attempt, flow rate 6 was nearly identical to flow rate 5. The flow control volume valve wasn’t adjusted correctly and this has effectively shortened our experimental range. This may have contributed
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unfavourably to our mean value of K. Flow rate 5 and 6 were both taken over a lesser volume, which may have led to some inconsistencies.
Conclusions and recommendations: The pressure difference across 6 bends and fittings were measured under differing flow rates to determine the loss coefficient K. The results were displayed on a graph of pressure drop over the velocity squared on twice the gravitational constant. Over the test that where carried out it was found that H increases with increasing Velocity squared for all bends and fittings. The tighter bends showed greater losses as the flow rate increased compared to the Expansion/contraction and the long bend. Overall the results were close to the published data. The exceptions being the expansion/contraction. For future experiments it is recommended to use the same volume for all test and to account for the relative elevations in the pressure difference calculations for the expansion and contraction.
Nomenclature: K D H Q A V V^2 g s z
Loss coefficient Pipe diameter Height of water in manometer Volumetric flow rate Area Velocity Velocity squared Gravitational constant (9.81) Liquid density Time in second Relative elevation
mm m m^3/s m^2 m/s (m/s)^2 m/s^2 kg/m^3 s m
References: Discover with Armfield (2010)., http://discoverarmfield.com/media/transfer/doc/f1.pdf Pipe fitting data base (2016).,http://www.pipeflow.com/pipe-flow-expertsoftware/pipe-flow-expert-software-screenshots/expert-screenshotspipes-fittings Potter, M.C., Wiggert, D.C., & Ramadam, B.H. (2012) Mechanics of fluids. Cengage learning .,11.2: p 544. Potter, M.C., Wiggert, D.C., & Ramadam, B.H. (2012) Mechanics of fluids. Cengage learning., Table 7.2: p 316.
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Vinidex technical manual (2013)., http://www.vinidex.com.au/wpcontent/uploads/2013/03/VIN014_PVC_Technical_Manual.pdf
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