3.2. Experimental Uncertainties
The experimental uncertainty include the combined effect of pipe dimensions (length and diameter) and the accuracy of flow rate measurement (collected water volume and time). The expected error for each parameter are given as: pipe diameter = ±0.02 mm, length of pipe = ±2 mm, water volume = ±5 ml and time for water collection = ±0.032 sec, manometer reading =± 10mm. These values are used to calculate the error in pressure drop and Reynolds number for each experimental point for non-coated pipes as the values for coated and half-coated pipes are very close to non-coated pipe. The error bars are added to non-coated pipes only in each figure to reflect the experimental uncertainty.

3.3. Variation of Pressure drop with Reynolds number

For 5mm pipe, as can be seen in Figure 2, the coated pipe shows an increase in pressure drop of 10 % when compared to the non-coated pipe. However, the discrepancy is small for Re < 5000, but increased with higher Reynolds number. It can be observed that the flow is turbulent for all data points.
Figure 3 presents the data for 4mm pipe. The results are in the range of transition and turbulent flow regime. It can be observed that the pressure drop for coated pipe is higher by 12% compared to non-coated pipe. The discrepancy increased for higher Reynolds numbers. The data of pressure drop for coated pipe shows a step increase for Re > 4170. This may be attributed to experimental error in measurement of one the variables. The increase in pressure drop for coated pipes of 5 and 4 mm may attributed to the a Wenzel wetting state [15] where the coating reduces the air gaps on the surface and increase the friction losses compared to uncoated surface.
The results for pressure drop in Figure 4 of coated and non-coated 3 mm pipes are much closer. The data from coated pipe is 3% lower than the non-coated pipe. The results from 3mm pipe in Figure 4 provides an interesting transition between the flow in pipes of 4 and 5 mm compared to flow in pipes 1 and 2 mm. The 3mm diameter can be considered as the boundary between the pipes that considered as small and the conventional pipes. This change in trend of drag reduction may be attributed to the increased effect of viscosity on the flow at the central zone of the small pipes compared to the large pipes. This finding is supported by the value of 3 mm for multiphase flow transition suggested by [12].
In Figure 5, the results for flow in 2mm pipe indicates pressure reduction due to the applied hydrophobic coating of 11.5%. This is in agreement with the work conducted by [5, 10 and 11]. It should be highlighted that all data points of the 2mm pipe were within the laminar flow regime. The only exception is the point with highest Reynolds number value which have passed into the transition flow regime.
The results of the 1mm pipe experiment, as seen in Figure 6, reveal a comparable relationship to that of the 2mm pipe. Thus, for laminar flow regimes in small pipes the apparent drag reducing effect of hydrophobic coating appears confirmed. The correlation between pressure and Reynolds number is clearly linear. An average drag reduction of 9% has been recorded.
In summary, the present data for laminar flow in the 1, 2 and 3 mm pipes show a reduction pressure drop for coated pipes which is support by a similar finding from the literature [2], [5], [11] and [13]. The main reason for this behaviour was attribured to the slip condition at wall due to the liquid-air wetting surface condition (Cassie-Baxter wetting state) at the pipe surface.
On other hand, the present data for transition and turbulent flow are in contradiction with the finding in the liturature given by [9] and [10]. This may attributed the difference surface topograhy [7] between present work and data from liturature. This means that the size and spaces of ridges and troughs are the controlling factor of drag increase/reduction by controlling the actual contact surface area between the liquid and the pipe surface and how much void trapped in the troughs. Based on the surface charactristics reported in [7], the increse in pressure drop in present work can be attributed to the reduction in voids at the wall and increase of direct contact between water and the pipe wall in turbulent flow regime.

Variation of pressure drop with percentage of coated pipe wall

Two cases for 2 mm and 4 mm pipes are investigated for 0, 50% and 100% coating. The 2 mm can be considered as small pipe and 4 mm as conventional pipe. The examination of half coated 4mm pipe seen in Figure 7 portrays more than 50% of pressure increase of the fully coated as the trend line is closer to fully coated pipe than non-coated. This is likely due to the effect of pipe wall surface the change in flow structure due to asymmetrical flow condition in the half coated pipe as shown by images. All of the data points are within the transitional and turbulent flow regimes. The increase in pressure drop may be attributed to the combined effect of reducing the size of air gaps on the surface by coating and removing the air from the gaps by the turbulence eddies which lead to direct contact between the water and pipe wall. This condition will create Wenzel wetting state which increase friction losses in coated pipe compared to uncoated pipe.
The 2mm pipe results, seen in Figure 8, show a strong similarity to that of the 4mm pipe with the half-coated data points being located between the coated and non-coated pipes. However, the data of half-coated pipe are very close to non-coated pipe compared to that of the coated pipe. This is in contrast to that observed for the turbulent in 4mm pipe. In this case, the asymmetry effect is more significant than the percentage of coated pipe surface.