3.7 Experimental Uncertainties
3.7.1 Friction Factor
The friction factor is given by the Darcy equation which is expressed mathematically as
(3.2)
The velocity term in this equation is computed as
(3.3)
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The flow area is given by
(3.4)
Therefore, the velocity can be written as,
(3.5)
Finally, the friction factor can be written as
(3.6)
From Eq. 3.6, it can be seen that the friction factor depends upon 1) pressure drop, 2)
inside diameter of the tube, 3) density of the fluid flowing through the tube, 4) length of
the tube, and 5) mass flow rate of the fluid.
The uncertainty of measuring the pressure drop, mass flow rate and the length of the tube
can be controlled depending upon the procedure of taking the data. However, uncertainty
in the tube diameter depends upon the manufacturer’s accuracy and methods.
The accuracy of the pressure transmitter is specified as +0.65% of span by the
manufacturer. While taking readings, careful attention was given so that the process
reached steady state and all of the three transducers were reading the same pressure drop.
However, when taking readings with water at low Reynolds number and higher tube
diameter, the uncertainty in the measurement of pressure drop seemed to be high which
were indicated by slightly different reading of the three pressure transmitters. The
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situation seemed better when using nanofluid as the working fluid. In this case the
readings from the lower range pressure transmitter were used for data analysis.
The uncertainty in the inside diameter of the test section is a major factor that affects the
measurement of friction factor. From equation 3.5 it is clear that the friction factor relates
to the fifth power of the inside diameter. The tolerance provided by the manufacturer is
±0.002 inches.
The accuracy of the mass flow meter is specified as ±0.05% of the flow rate. Here also
extra attention was given to capture a steady state process.
The uncertainty of the tube length is determined by the accuracy of the measurement
scale used for measuring the tube. The least count of the measurement scale used is ±
0.25 inches. Repeated measurements were taken to avoid any error. The uncertainty for
the length of the tube is given as ± 0.25 inches.
The nanofluid density is taken as 1.19 gm/cc. The operating range of the experiment was
from 5°C till 70°C. It is assumed that the particle density stays constant over this range
whereas the density of water may change slightly. The maximum uncertainty in density is
calculated as 1.69%.
The uncertainties of the friction factor were estimated within ±5.65 to ±8.53%, as shown
in Table 3.1.
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