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 90q 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
ݍ୫ = ߩ ܳ = ߩ ݓ ܣ
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:
Re = ߩ ݓ᩸݀
ߤ
= 4 ݍ௠
ߨ ݀ ߤ
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 )
݂ = ଴.ଷଵ଺ସ
ୖୣభ/ర
Frictional pressure loss
ȟ݌௙ = ݂ ௅ௗ ᩸ଵଶ ߩݓଶ
2Calculate 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
flow
Average
velocity
Reynolds
number
Friction
factor
Measured pressure losses Theoretical
straight pipe
qm w Re f 'p12m 'p23m 'p34m 'p14m 'p12fc 'p14fc
[kg/s] [m/s] [Pa] [Pa] [Pa] [Pa] [Pa] [Pa]
15.06 1.45 14 000 0.035 1 300 800 1 400 3 500 1 350 3 200
15.10 1.47 14 300 0.034 1 310 805 1 420 3 534 1 360 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:
߂݌bend ൌ ο݌ଵସ୫ െ ο݌ ଵସ୤ୡ
Definition of minor loss coefficient:
߂݌bend = ܭbend 12ߩݓଶ
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.)
US
meter
Reynolds
number
Minor
loss
Rough
estimate
qm Q Re Kbend Kbend
[kg/s] [L/min]
15.06 14.89 14 000 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).
3Measurement 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.