# Feasibility of Optical Flow Field Measurements of the Coolant in a Grinding Machine
## 4 Measurement Results
### Feasibility of PIV to Measure the Laminar MWF Flow Velocity \(v_{\mathrm{sup}}\)  
PIV velocity field measurements are taken for top and side view of the laminar MWF supply flow with a flow rate of \(14.9\,\mathrm{L/min}\). The average 2d velocity fields and their corresponding uncertainties for jet positions from \(x=40\,\mathrm{mm}\) to \(120\,\mathrm{mm}\) according to top and side view are shown in Figure 6. The flow directions are indicated by the vector directions and the background displays the colour-coded magnitude of the 2d flow field \(v_{\mathrm{sup}}\) in m/s.  
The measurement from the top view reveals a homogeneous velocity field along the \(x\)-axis. In the middle area from \(y=-5\,\mathrm{mm}\) to \(5\,\mathrm{mm}\) the velocity is constant along the whole \(x\)-axis at \(5.55\,\mathrm{m/s}\). In contrast, the bottom edge of the flow (\(y=-5\,\mathrm{mm}\) to \(-10\,\mathrm{mm}\)) shows a systematically lower velocity of \(5.4\,\mathrm{m/s}\). This difference in the measurement can be caused by the cylindrical edge, which is responsible for possible light deflections. To exclude systematic measurement errors due to light deflection, the following analysis focuses on the homogeneous range from \(y=-5\,\mathrm{mm}\) to \(5\,\mathrm{mm}\).  
The uncertainties of the measurements increase, when the signal-to-noise ratio decreases due to poor illumination. The area from \(x=60\,\mathrm{mm}\) to \(100\,\mathrm{mm}\) is well illuminated and shows a standard deviation of \(0.2\,\mathrm{m/s}\) for the velocity magnitude. In the poorer illuminated region, the standard deviation increases to \(0.6\,\mathrm{m/s}\). Hence, PIV measurements of the laminar MWF supply flow are achieved with a standard deviation of approximately 4% in the well illuminated region despite the difficult measurement conditions regarding accessibility and the influence of light refraction.  
Subsequently, the measurements of top and side views are compared to identify systematic influences of light refraction. Unlike the top view, the measurements from the side view show a linear decreasing velocity from \(5.6\,\mathrm{m/s}\) to \(5.4\,\mathrm{m/s}\) with a constant standard deviation of \(0.2\,\mathrm{m/s}\). For better illustration of the flow velocity along the \(x\)-axis, the average along the \(y\)-axis is calculated and displayed in Figure 7 for the top view and the side view. The average velocities along the \(x\)-axis are displayed as a solid line and their standard deviation as the coloured background.  
The top view shows a constant average velocity of \(v_{\mathrm{sup}}\ =5.55\,\mathrm{m/s}\) without any significant changes along the \(x\)-axis. In comparison, in the side view at first a small increase from \(5.6\,\mathrm{m/s}\) to \(5.64\,\mathrm{m/s}\) is measured, until it decreases almost linearly to \(5.4\,\mathrm{m/s}\). The differences in the velocity are attributed to the observation of seeding particles through the curved surface of the cylindrical edges. Due to light deflections, a systematic position deviation between the observed and original position of the tracer particles occurs, which leads to systematic measurement deviations for the position and thus also for the velocity. Although the side view measurements are systematically affected by light refraction, the differences between the measurements of both views are mostly smaller than \(0.1\,\mathrm{m/s}\). Therefore, flow field measurements on the laminar MWF supply flow with PIV for top and side view are feasible.