lossesinbendsandfittings
Losses in Bends and Fittings
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Institution
Date
Contents
Changes in Cross Sectional Area. 4
Using Area Reduction (Metering Constrain) to plot the Calibration Curve. 5
Position characteristic Curve. 6
Resistance coefficients of bends and elbows. 7
Changes in Cross Sectional Area. 10
Table 1 Re coefficient look up table. 4
Table 2 Kinematics Viscosity table. 5
Table 3 wall roughness look up table. 5
Table 4 Resistance coefficient table for bends. 6
Figure 1 Reducer calibration curve. 8
Figure 2 Point Characteristic Curve. 9
Introduction
Pipes with several types of fittings and varying cross sectional dimensions tend to have head losses. This also depends on frictional factors and volumetric flow rates of the fluid (Rahmeyer, 1999). These variables can induce turbulences and eddy currents into the systems and result to a potential loss in pressure. This is detrimental to the overall efficiency of piping systems. Hence this experiment was setup to investigate the pressure lost in fittings/elbows and compare the losses. The experiment also aimed at observing various valve characteristics by looking at enlargements and reductions and their correlation to pressure loss. The HM 150 module wad used to simulate various conditions in a bid to investigate these pressure losses.
Theory
Pipes are extremely important within the chemical engineering industry and play a vital role of transferring fluid from A to B around a chemical plant. For fluids to flow, they require a driving force known as a pressure gradient. The inlet pressure must be larger than the outlet pressure to allow for the fluid to flow. Pipelines consist of straight lengths of pipe punctuated by a number of fittings. There are also many different types of valves that can be implemented and each valve controls the flow rate in different ways. These inline components and many more typically affect the pressure and flow rate of the fluid.
Resistance coefficient
Reynolds’ number (Re) was derived by Nikuradse and Colebrook to quantify the turbulences induced by in line components and the roughness of the carrier surface (Camille Duprat, 2015). When Reynolds’ number (Re) is more than 2320 it means the flow path is prone to turbulences at varying levels (J. Happel, 2012). In other words, the pipe has a friction coefficient (λ) than varies with Re and the level of roughness in the flow path. This level of roughness (K) depicts the depth of the wall elevations or the pipe diameter d. Different test pipes exhibit different roughness values. According to Nikuradse and Colebrook, there is a correlation between Reynolds’ number (Re) and roughness as shown below (J. Happel, 2012).
Table 1 Re coefficient look up table
Reynolds’ number (Re) can be calculated using fluid velocity, the pipe diameter (d) and the kinematic viscosity v.
R_{e}=
The fluid velocity is obtained from the volumetric flow V
v =
While the kinematic viscosity is a function of temperature and it can be derived from tables (Kalide, 2015).
Table 2 Kinematics Viscosity table
There are also special fittings such as curves, bends, valves and cross sectional dips that cause pressure changes in addition to losses attributed to wall friction. For instance, changes in cross sectional area results to changes in fluid velocity. Therefore the Bernoulli equation is used to account for the total pressure losses (Stephen Londerville, 2013).
(
Total level loss is also obtained as
(
However, for ease of calculations, empirical values of resistance coefficients (ᶉ) for various elements are provided in books (Kalide, 2015).
Thus; after getting the resistance coefficients the pressure loss is calculated as;
And loss level is given by;
For bend pipes, there is a correlation between the resistance coefficient and shape of the bend and ratio of bend radius to pipe diameter
The resistance coefficient can be obtained from the curve below
Table 4 Resistance coefficient table for bends
Changes in Cross Sectional Area
A discontinuous enlargement or reduction of the Cross sectional area leads to a change in flow resistance. The coefficient of resistance of an enlarged or reduced cross sectional area can be obtained using Bernoulli principle of linear momentum (Camille Duprat, 2015).
In case of an enlargement
ᶉ =
In case of a reduction
ᶉ =
Procedure
Part 1
Required plotting a graph of pressure drop against velocity to produce a calibration curve. This involved finding the pressure drop across the severe reduction section at different flowrates.
Part2
Entailed producing the characteristic curve for various elements in the pipeline. This required measuring the pressure drop for individual components at fixed flowrates.
Part 3
Involved measuring the pressure all four corners of the system at a fixed flowrate and finally calculating the resistance coefficients.
Precautions
It was statutory to ensure both the entrance and bowl valve were closed before switching the pump on or off. This was important because if the valves were open, the water in the system could goes back leaving air inside the pipe system that could cause error readings in the manometer. The same was to be done when removing air bubbles when setting the manometer.
The manometer was to be reset whenever the hose connector was attached to a new measurement point. This was important for part1 and 3 of the experiment.
Experiment
Using Area Reduction (Metering Constrain) to plot the Calibration Curve
The HM 150 module has a reducer with a severe area reduction. This reduction produces an effect akin to a metering orifice, hence this fitting can be used to generate a calibration curve (Kalide, 2015).
In this experiment the curve was obtained by plotting the reduction in pressure ∆p (mmWs) against the flowrate V (1/min) induced into the orifice. The first volumetric flowrate used was measured in the HM 150 module tank and the corresponding pressure was readings were obtained from the manometers. The spherical valve was used to adjust the volumetric flowrate and the corresponding values of pressure loss were recorded.
Results
The Reducer Calibration Curve  
Loss in Pressure ∆p (mmWs)  Flowrate (I/min) 
250  6.18 
170  5.142 
120  4.14 
Graph
Figure 1 Reducer calibration curve
Position characteristic Curve
The spring tube manometer can be used to record a characteristic curve for all points. Thus the pressure fluctuations for all objects could be determined by plotting the pressure changes with respect to various positions (Kalide, 2015).
Results

Flowrate (I/min)  
23.076  21.42  24  
Point  Pressure (bar)  
1  0.45  0.42  0.39 
2  0.42  0.39  0.35 
3  0.40  0.38  0.35 
4  0.15  0.12  0.10 
5  0.15  0.12  0.11 
6  0.12  0.10  0.10 
7  0.10  0.10  0.09 
8  0.09  0.09  0.06 
9  0.07  0.06  0.05 
10  0.05  0.05  0.04 
11  0.04  0.02  0.01 
V=23.076 (l/min)
Figure 2 Point Characteristic Curve
Resistance coefficients of bends and elbows
The aim of this setup was to investigate the pipe elbows in the circuit and how they contribute to pressure loss. All elements were observed one at a time and level losses were recorded at each point. The volumetric flow was set at maximum level and the manometer was set up to measure varying pressure changes across the bends.
Results
Type of fitting  Flow rate V (l/min)  Pressure loss in bars 
Pipe elbow +90^{0 }, d= 17mm  23.076  0.44 
Round bend 90^{0}, d= 17mm  23.076  0.14 
Narrow pipe bend 90^{0}, d= 17mm, r=40mm  23.076  0.1 
Wide pipe bend +90^{0}, d= 17mm, r=100mm  23.076  0.06 
Calculations
Narrow pipe bend,
Resistance coefficient
ζ can be estimated using the pipe radius/diameter ratio.
R/d = 40/17 = 2.35
A PVC has a wall roughness coefficient of 0.0015 hence it is considered a smooth surface.
From the graph the ratio indicates ζ = 0.12
Mass flow v= 23.076 l/min
The kinematic viscosity of water assuming fluid temperature of 20^{o}c is 1004 × 106 m²/s
Pressure loss (kg/m^{2})
Pressure loss can be obtained from the formula
Where:
= Resistance Coefficient
p = Density of 998 (kg/m^{3})
ω = Flow Velocity (m/s)
But fluid velocity is calculated as
ω =
Where:
V = volumetric flow rate (l/min)
D= diameter of pipe (m)
Converting the volumetric flow rate to m^{3}/s units leads to
23.076/60000 = 0.0003833 m^{3}/s
Hence ω = = 1.689 m/s
Therefore
mbar
 Loss level
Loss level (kg/m^{2})
Loss level can be obtained from the formula
= 0.171 kg/m^{2}
= Resistance Coefficient (determined by test or vendor specification)
p = Density of 997 (kg/m^{3})
ω = Flow Velocity of 23.076 l/min
Wide pipe end
R/d = 100/17 = 5.88
From the graph a value of 5.88 gives
 Resistance coefficient can be obtained from the graph. ζ = 0.09
 Pressure loss can be obtained from the formula = 1.28mbar
 Loss level can be obtained from the formula = 0.12 kg/m^{2}
Round bend
90^{0}, d= 17mm
 Resistance coefficient ζ of 1.3
 Pressure loss can be obtained from the formula = 18.51mbar
 Loss level can be obtained from the formula = 1.85 kg/m^{2}
Reynold’s number
Reynold’s number Re can be obtained
R_{e}=
Where
D= diameter
W = flow velocity
V= kinematic viscosity
R_{e}= = 28.6
Discussion
The pressure loss results obtained above can be used to justify theoretical knowledge.
 Resistance depends on the deflection angle
 Resistance depends on the ratio between the radius of the pipe aperture and cross sectional diameter of the pipe.
Highest resistance is noted at the pipe elbow because it has a sharp edge. Directional changes in the sharp end causes the highest rippling effect hence resistance increases and pressure attenuates significantly. Also as the ratio of bend radius to diameter of the pipe increases, the resistance decreases and less pressure is dropped.
Changes in Cross Sectional Area.
The experiment was setup to investigate the effects of the enlarger and the reducer on pressure changes. A constant flow rate was set to flow into the fittings. The manometer was also connected across the circuit. The measurements were performed and the pressure changes recorded.
Results
Fitting  Flow rate in l/min  Loss Height in mm 
Reducer, d= 17mm to d=9.6mm  6.18  250 
Enhancer, d=9.6mm to d= 17mm  6.18  10 
Calculations
Enlargement
Resistance coefficient
ᶉ =
Therefore
ᶉ
Hence resistance coefficient ᶉ
Pressure loss
Pressure loss can be obtained from the formula
But fluid velocity is calculated as
ω =
Where:
V = volumetric flow rate (l/min)
D= diameter of pipe (m)
Converting the volumetric flow rate to m^{3}/s units leads to
6.18/60000 = 0.000103 m^{3}/s
Hence ω =
Velocity of flow = 1.43 m/s
Velocity of flow2 = = 0.45 m/s
Loss level
Loss level can be obtained from the formula
= 0.393 kg/m^{2}
Reynold’s number Re
Re can be obtained
R_{e}=
Where
D= diameter
W = flow velocity
V= kinematic viscosity
R_{e}= = 7.62
Reduction
Resistance coefficient
ᶉ =
Therefore
ᶉ
Hence resistance coefficient ᶉ
Pressure loss
Pressure loss can be obtained from the formula
But fluid velocity is calculated as
ω =
Converting the volumetric flow rate to m^{3}/s units leads to
6.18/60000 = 0.000103 m^{3}/s
Hence ω_{, }Velocity of flow = = 0.45 m/s
Velocity of flow2 = = 1.45 m/s
Thus
Loss level
Loss level can be obtained from the formula = 0.12 kg/m^{2}
= 4.66 kg/m^{2}
Reynold’s number
Re can be obtained
R_{e}=
Where
D= diameter
W = flow velocity
V= kinematic viscosity
R_{e}= = 24
Discussion
Very little pressure loss in observed on the area enlarger. In other cases there might be an increase in pressure at the enlarger when a loss in speed leads to an increase in pressure that surpasses the pressure lost due to friction in the path.
Conclusion
This experiment was purposed to investigate pressure losses in fittings and elbows. The experiment also looked into effects caused by valves and reductions or enlargements in pipe cross sectional diameter. The HM 150 unit was used to simulate these minor losses by illustrating the turbulent effects on pressure induced by the stated variables. The experiment confirmed that resistance depends on the deflection angle and radius of the pipe aperture. Highest resistance is noted at the pipe elbow with the sharpest edge. The experiment also investigated effects of sudden area reduction and enlargement with the highest drop being observed in the reduction point.
Works Cited
Camille Duprat, H. A. (2015). Fluid Structure. Royal Society of Chemistry.
 Happel, H. B. (2012). Low Reynolds number. Springer Science & Business Media.
Kalide. (2015). Losses in Bends and Fittings. Einführung in die technische Strömungslehre, 26.
Rahmeyer, W. J. (1999). Pressure Loss Coefficients. American Society of Heating, Refrigeration & AirConditioning Engineers.
Stephen Londerville, C. E. (2013). Combustion Handbook. CRC Press.
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