MINOR LOSS COEFFICIENT OF PIPE BEND
Pressure differences in pipe are measured in locations indicated in the figure below. The distances are: L1 = 500 mm, L2 = 100 mm, L3 = 100 mm and L4 = 500 mm. The pipe diameter is constant and the pipe is located horizontally.
The aim of the work is to determine the minor loss coefficient Kbend of 90 bend. Measurements are performed at least with three mass flow rates.
Mass Flow Rate
Mass flow rates are determined based on mass of water incoming to a bucket in 60 seconds. They are then used as reference values. Mass flow rate is obtained as a product of density and volume flow rate
= =
Average velocity and Reynolds number
The pipe cross-sectional area A is calculated with the known inner diameter of the pipe. The average velocity w can be calculated from density, area and mass flow rate. Reynolds number Re for pipe flow is defined as follows:
Please note that temperature affects significantly to water viscosity (see e.g. White F.M. 2005: Fluid Mechanics, Table A.1 p. 810).
Pressure loss in straight pipe
Friction factor f for a smooth pipe can be calculated with Blasius correlation (turbulent flow and Re < 105 ) = .
Frictional pressure loss
=
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Calculate theoretical pressure loss p12fc for the first part 1-2 and compare results to measured values p23m and p34m (parts 1-2 and 3-4). Calculate theoretical friction pressure loss extended to entire pipe length p14fc 1-4 (Ltot = L1 + L2 + L3 + L4 = 1.200 m) based on part 1-2. Draw a chart of different calculated and measured pressure losses (1-2, 2-3, 3-4 and 1-4) as a function of the average velocity w. Present results in the form of Table 1, where values now are arbitrary. Comment possible differences.
Table 1. Measured pressure losses (subscript m) vs. calculated frictional pressure losses (subscript fc) for a hydraulically smooth straight pipe.
Mass Average flow velocity
qm w [kg/s] [m/s]
15.06 1.45 15.10 1.47
Reynolds number Re
14 000 14 300
Friction factor f
0.035 0.034
Measured pressure losses
Theoretical straight pipe
p12m [Pa]
1 300 1 310
p23m p34m [Pa] [Pa]
800 1 400 805 1 420
p14m [Pa]
3 500 3 534
p12fc [Pa]
1 350 1 360
p14fc [Pa]
3 200 3 210
Minor loss coefficient of pipe bend Kbend
Measured pressure difference p14m was higher than calculated friction pressure loss p14fc.
This is due the minor loss of pipe bend:
bend 1
Definition of minor loss coefficient:
bend = bend 2
Calculate a rough estimate for the minor loss coefficient using measured pressure difference p23m and comment possible differences. In addition to the mass flow measurement with a bucket, the volume flow rate Q was measured with an ultrasonic (US) flow meter. Compare the results of these two methods and discuss reasons of possible differences.
Table 2. Comparison of mass flow rates and minor loss coefficients.
Bucket (ref.) qm
[kg/s] 15.06
US meter Q [L/min]
Reynolds number Re
14 000 …
Minor Rough loss estimate
Kbend Kbend 0.50 0.60
Present in graphical form pipe the bend minor loss coefficient Kbend as a function of Reynolds number. Compare the results to literature (at least from two different sources).
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Measurement report
Reference template (Thesis template – Word) for the report can be found from elut: https://elut.lut.fi/en/completing-studies/theses/bachelors-thesis
In this laboratory report abstract can be omitted. The date should be included in the cover page.
Attention should be paid to the presentation accuracy of the results. Uncertainty analysis should be included in the report. The measurement document (protocol) should be added to appendix.
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