Error Analysis

Errors between the theoretically calculated values for differential pressure and the measured

values would have resulted from multiple reasons, listed below:

- Systematic errors,

- Procedural errors and,

- Human errors.

Systematic errors relate to the actual physical experimental gear. The experiment composed

of an aperture, with a single entry and exit, which housed a fan, pressure monitoring sensors,

and an orifice at the exit. The aperture is susceptible to tears, may not be airtight, or may have

an imperfect connection, all resulting in additional intake/outtake airflows affecting measured

values.

At the beginning of testing the three fan speeds, the entire system was recalibrated, all

sensors were zeroed, and the orifice was open to its largest diameter. However, there are

possibilities that the sensors would not zero properly as there was no control taken; variations

in atmospheric pressure, and inconsistencies in flow behaviour due to human movement

around the experimental set up.

Procedural errors relate to the inconsistencies between each trial. For each trial, the system

was allowed to equilibrate, which involved allowing consistent airflow through the duct for a

few seconds (10-15 seconds). Errors would arise as the system would not have been allowed

to equilibrate appropriately, resulting in inconsistent measurements.

Human errors relate to how the experiment is conducted. Therefore, errors that would stem

from human error could have affected any aspect of the experiment, from its physical set-up,

its conduction, and measurement.

4.0 Conclusion:

Bernoulli's equation, derived from Reynold's transport theorem (which assumes the

conservation of mass and energy), provides a relation between differential pressure and

volumetric flow rate for any fluid flow. Fundamentally, it shows the inversely proportional

relation of the two; an increase in volumetric flow rate results in a decrease in differential

pressure, and vice versa. This was consistent with the fan performance results as displayed in

graph 1.

Dimensional analysis is a highly efficient/effective way of analysing multivariate factors

within two or three non-dimensional coefficients. Therefore, it was used to model the fans

performance to be able to obtain differential pressure or volumetric flow rate values that

could not be experimentally obtained. Dimensionless coefficients, flow () and head (),

were plotted to model the fans performance.

To assess the feasibility of using the dimensionless coefficients to obtain values for the

differential pressure/volumetric flow rate, three pre-determined flow coefficients were chosen

and their subsequent differential pressure were calculated. Minute errors between the

theoretical and measured values were present, however all the potential error sources were

identified and examined, therefore it can be concluded that the theoretical values provide a

fairly accurate approximation.