Major And Minor Losses Due To Pipe Diameter And Fitting - Lab Report PDF

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Campbell 1

Major and Minor Losses Due to Pipe Diameter and Fitting Kade Campbell

Abstract

L

onger pipe with a smaller diameter and several types of fittings is bound to have high head losses and high frictional factors for many different volumetric flow rates. Experimentally, two sections of pipe with diameters of 0.43 and 1.025 inches and a length of 5 feet were used to find major losses in a system. The smaller diameter consistently produced a higher frictional factor, ranging from values of 0.0302 to 0.0372, compared to values ranging from 0.0240 to 0.0295 for the larger diameter. This is due to the higher ratio of the surface area of the pipe to the cross sectional area. This higher frictional factor corresponds to a higher head loss within the pipe as well. When four different elbow fittings, a sudden expansion fitting, and a sudden contraction fitting were attached to a pipe and a fluid flowed throughout, minor losses due to the fittings were found. Data analysis of the experiment proved that the longer the bend, the lower the minor loss coefficient (K) was, which resulted in an experimental value of 0.357 for the longer elbow. The miter bend, or the 90⁰ bend, produced an experimental value of 1.11. While theoretically a sudden expansion usually produces a higher K value than a sudden contraction, the experimental values displayed opposite results. The sudden expansion resulted in a K value of 0.177, while the sudden contraction produced a K value of 0.755. Keywords: Head loss, pipe fittings, frictional factor, minor loss coefficient.

Introduction By know the major head losses due to pipe diameter over a length of pipe and the minor head losses caused by pipe fittings can cut down on cost and raise the overall efficiency of a system. Calculations to determine system pressure drop require experimental data to account for friction losses occurring in valves and fittings (Steffe and others, 1984). Several experiments have been performed in order to help reduce minor and major losses through systems involving orifice meters and pipe sections with various fittings. Orifice meters are simple and inexpensive differential pressure flow meters used throughout many industries and applied to a wide range of liquids and gases (Ramirez and others, 2013). Factors such as the types of fittings used, diameters and lengths of the pipe, and material of the pipe are all important aspects to know. The goal for every project involving piping is to maintain the highest efficiency and keep the losses due to the pipe and fitting at a minimal. Whether that be for irrigation purposes, food processing, chemical transport, or other various real world uses, head losses due to frictional factors need to be kept low.

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Objective The objective of this experiment is to measure the effects that pipe diameter have on the friction factor, or major losses, and the effects that various fittings have on the minor losses in pipes.

Materials and Methods Major Losses To find the major losses throughout the system, a Technovate fluid circuit system was used. The pressure losses across two sections of pipe, with inner diameters of 0.43 and 1.025 inches, and across an orifice were found. By Cd having value of 0.656, the volumetric flow rate (Q) can be found using equation 1 below. (Eq. 1 𝑄 = 𝐴𝑜 𝐶𝑑 √

2∆𝑃𝑜𝑟𝑖𝑓𝑖𝑐𝑒 𝜌(1 − 𝛽4 )

Where: Q=Volumetric Flow Rate Ao=Cross-Sectional Area of the Orifice Cd=Discharge Coefficient ∆Porifice=Pressure drop across the orifice Ρ=Density of the fluid β=Ratio of throat diameter to pipe diameter

Ranging from 5 to 25 inches, 6 readings at different flow rates were obtained with the pressure differences across the orifice being used to calculate Q. The pressure losses across the two sections of pipe (head loss, hL) is used to find the Darcy friction factor (f) for the sections of pipe. The value for hL is obtained by diving the pressure drops across the sections of pipe by the product of the density (kg/m3) of the fluid and gravity (m/s2). Using equation 2 below and known values, the friction faction can be calculated. 𝐿 𝑉2 ℎ𝐿 = 𝑓 𝐷 2𝑔

Where: hL=head loss due to pipe 𝑓 = Darcy’s friction factor L=Length of the section of pipe D=Diameter of the section of pipe

(Eq. 2

Campbell 3 V=Velocity of the fluid through the pipe, where V=Q/A g=gravity In order to calculate the theoretical values for the friction factor, the Colebrook equation (Cengel and Cimbala, 2014), shown below as equation 3, is calculated while using known values. (Eq. 3 1

√𝑓

= −2.0 log (

𝜀 ⁄𝐷 2.51 ) (𝑡𝑢𝑟𝑏𝑢𝑙𝑒𝑛𝑡 𝑓𝑙𝑜𝑤) + 3.7 𝑅𝑒√𝑓

Where: 𝑓 = Darcy’s friction factor 𝜀 = Roughness D=Diameter of the section of pipe Re=Reynolds number of the fluid With the pipe being made of copper, the roughness value is 0.0000015 m. Minor Losses To find minor losses, an Edibon Energy Losses in Bends module was used with various fittings throughout the system. The types of fittings and pressure drops across each include a long elbow measured by manometers 1 & 2, sudden expansion displayed by 3 & 4, and a sudden contraction displayed on 5 & 6. There was a medium elbow displayed on 7 & 8, a short elbow measured on 9 & 10, and a right angle fitting (miter bend) measured on manometers 11 & 12. By using the control valve and changing the flow rate, the volumetric flow rate through the system can be calculated by measuring the initial and final volume of the water reservoir after one minute. Six measurements of each manometer were taken for every change in flow rate conducted. The minor head loss is obtained for each flow rate across each fitting by dividing the pressure drops across each fitting by the product of density and gravity. After plotting the head losses versus the square of the velocities, the minor loss coefficient (K) can be found using equation 4. 𝑉2 ℎ𝐿 = 𝐾 2𝑔

(Eq. 4

Campbell 4 Where: hL=Head loss due to the pipe K=Minor loss coefficient V=Velocity of the fluid through the pipe g=Gravity

Results and Discussion Major losses With the head loss of each section of pipe being the pressure drop across the pipe divided by the product of the density of the fluid and gravity, equation 2 can be used to calculate the experimental friction factor for each flow rate. By using the Colebrook equation and the Excel function Goal Seek, the theoretical values were found. The Goal Seek function is carried out by setting the cell that contains the Colebrook equation to equal zero by changing the cell that contains the friction factor. The theoretical and experimental friction factors were plotted versus the square of the velocity through the pipe for the larger and smaller diameter sections of pipe shown in figure 1 and 2, respectively.

0.035

Large Pipe Friction Factor (f)

0.030 0.025 0.020 0.015 0.010

Theoretical

0.005

Experimental

0.000 0.3

0.4

0.5

0.6

V2

0.7

0.8

0.9

(m2/s2)

Figure 1: Friction factor of the larger diameter pipe versus the square of the velocity for both the theoretical and experimental values of “f”

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Small Pipe Friction Factor (f)

0.035 0.030 0.025 0.020 0.015 0.010

Theoretical

0.005

Experimental

0.000 0.3

1.3

2.3

3.3

4.3

5.3

6.3

V2 (m2/s2) Figure 2: Friction factor of the smaller diameter pipe versus the square of the velocity for both the theoretical and experimental values of “f”

The experimental friction factors for every flow rate were consistently higher that the theoretical values. This can be explained by saying the theoretical values are unable to take into effect any environmental factors within the pipe other than the material of the pipe itself. Some examples of environmental factors include but not limited to a fouling factor on the inside of the pipe accumulated over time, temperature of the fluid, though it will only affect the density of the fluid minimally. The diameter of the pipe affects the friction factor by the smaller diameter pipe causing an increase at low velocities with a gradual decrease as the velocity of the fluid increases. The larger diameter pipe begins at a lower friction factor while also seeing a gradual decrease as velocity of the fluid decreases. The smaller diameter pipe having a larger friction factor is caused by the 3:1 ratio of the surface area of the inner pipe to the cross sectional area of the pipe for the two given sections when comparing the smaller to larger, respectively. Minor Losses Using the Edibon Bends Module, the pressure drop across several fitting were measured and displayed onto 12 manometers. After plotting the head losses across each fitting versus the square of the velocities that the measurements were taken at, the minor loss coefficient (K) was found based on the slopes of the graph. The slope of the linear trendlines for each fitting is then multiplied by 2 and by gravity for the experimental values. Cengel and others provide the theoretical values for K for all of the fittings used during the experiment.

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0.040 y = 0.0564x Mitre

Long Bend

0.035

y = 0.0385x Narrow

Widening

0.030

hL (m)

Narrowing y = 0.0369x Short Bend

0.025

Elbow

0.020

Short Bend y = 0.0182x Long Bend

Mitre

0.015 y = 0.0214x Elbow

0.010 0.005

y = 0.009x Widening

0.000 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

V2 (m2/s2) Figure 3: Head loss (hL) due to the pressure drop across each fitting versus the square of the velocity for various flow rates

Table 1 below displays the theoretical and experimental K values. The miter bend and all three elbows show that as the bend is lengthened and straightened out, the K value reduces symbolizing lower pressure drops throughout each particular fitting. Experimentally, the sudden expansion produces a lower K value than the sudden contraction, which in return represents a lower pressure drop across the fitting. Table 1: Experimental and theoretical K values and percent error

Fitting Long Bend Widening Narrowing Elbow Short Bend Miter

Slope 0.0182 0.009 0.0385 0.0214 0.0369 0.0564

K Value Experimental Theoretical 0.357084 0.25 0.17658 0.5906 0.75537 0.4 0.419868 0.5 0.723978 0.74 1.106568 1.1

% Error 42.83 70.10 88.84 16.03 2.17 0.60

Campbell 7 The percent error between theoretical values and the experimental values are high in certain fittings, such as the sudden expansion and sudden contraction, because the theoretical values cannot take into friction al losses in addition to the flow being restricted to the vena contracta region . Theoretically, the losses in expansion usually are much higher than during contracting due to separation in flow (Cengel and others, 2014). Experimental values for the sudden expansion are lower than that of the contraction process, which can be a cause of human error while operating the Edibon system. Other than the long bended elbow, the percent error for each elbow are considerably low, but still consist of high K values. When concerned with turning space for placing pipe, the K value can be greatly reduced by added vanes around each bend to guide the fluid throughout. The theoretical value for each elbow also does not take into account the frictional losses along each bend, providing support for a difference between the theoretical and experimental values.

Conclusion The major losses were calculated for two sections of pipe with different diameters using the flow rate through a Technovate fluid circuit system. The smaller diameter pipe produced a higher friction factor across the section which was caused by the higher ratio of the surface area of the inner pipe to the cross sectional area. The frictional factor for the smaller diameter for various flow rates ranged from 0.0302 to 0.0372. The frictional factors for the larger diameters ranged from 0.0240 to 0.0295. The minor losses were found by calculated the pressure drops across various pipe fittings on the Edibon Energy Losses in Bends Module. It was concluded that the longer and more gradual turn in an elbow caused a lower minor loss coefficient (K=0.357) than a sharp miter bend (1.11). Also, experimental values for contraction and expansion fittings (Kcontract=0.755 and Kexpansion=0.177, respectively) and produced opposite results than the theoretical K values calculated. The theoretical K values for contraction and expansion are 0.40 and 0.59, respectively.

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References Cengel, Y.A., Cimbala J.M. (2014). Fluid Mechanics: Fundamentals and Applications, (pp. 367, 393395). New York City, New York: McGraw-Hill. Ramirez, B. C., Maia, G. D. N., Green, A. R., Shike, D. W., Gates, R. S., Rodriguez, L. F. (2013). Design and validation of a calibrated orifice meter for sub-500 liter per minute flow rate applications. 2013 ASABE Annual International Meeting Paper. Vol. 1. Pages 1-4. Steffe, J. F., Mohamed, I. O., Ford, E. W. (1984). Pressure Drop Across Valves and Fittings for Pseudoplastic Fluids in Laminar Flow. Transactions of the ASABE. Vol. 27. Pages 616-619....