## 2 Materials and Methods  
In a Poiseuille flow channel configuration, it is known that the magnetic field would generate a pressure difference and regulate the pressure drop, as occurs in the valve operating mode [28]. However, in a Poiseuille flow arrangement, the pressure difference is generated because the existing fluid flow is obstructed and thus, the measured pressure difference is identified as flow pressure drop occurs due to obstruction. The valve mode of the MRFs, for example, examined the magnitude of the pressure drop as a proportional contribution of the magnetic field strength and the yield stress of the fluid. On the other hand, the pressure measurement arranged in this paper is intended to observe the possibility of the magnetic field to generate pressure to the MRFs when it is at rest. Therefore the nature of the measurement is different from the measurement conducted at the valve mode arrangement. In this study, the observation will be conducted using a U-shaped tube arrangement. The U-shaped tube method was chosen due to its simple pressure measurement process [29], as unequal pressure in the legs of the tube will result in different liquid levels, which indicate a pressure difference in the channel of the U-shaped tube. The U-shaped tube would be initially set at rest, with balanced pressure between both legs without a magnetic field. Once the liquid in both legs is level, the magnetic field is slowly applied by increasing the current input to the coil. The liquid levels are observed to see whether there were changes in the liquid levels in both legs when the magnetic field was applied. Figure 1 showed the reaction of the MRFs in the U-shaped tube when an external magnetic field was applied, and there is a clear difference between the liquid levels of both legs, which indicated a change in pressure. The level change, in this case, is caused by the magnetic induction to the magnetic particles immersed in the MRFs that provides magnetic force attraction to the particles until it each reach equilibrium position. In order to quantify the observation, the magnetic field need to be estimated because it is not possible to insert the Gaussmeter probe in the U-shaped tube arrangement. The magnetic field estimation is conducted using FEMM an open-source software, 2-D finite element software widely used in magnetic analysis and simulations [11; 30; 31; 32; 33]. The FEMM simulation was carried out to simulate the magnetic circuits that exist in the theoretical model of the U-shaped tube apparatus. The material properties involved in the magnetic circuit are also used in the calculation, including the B-H curve values of the MRFs. To verify the accuracy of FEMM in estimating magnetic field strength a Gaussmeter test was also carried out on the upper surface of the coil on the axis of the coil hole, as shown in Figure 2a where measurements were possible. Figure 2b shows the observation point and magnetic field contour of the FEMM simulation. The observation point is 1 mm above the coil line due to the thickness of the bobbin that has been used. From the test result with Gaussmeter and FEMM Simulation, a comparison of results is obtained as shown in Figure 3. Based on the data obtained, that the simulation results are close to the measurement results, with an average error of 3%. Similar methods have been used in previous studies, such as in [11; 30; 33]. Figure 1: Different MRFs levels in both legs indicating a pressure change. Figure 2: FEMM verification setup, (**a**) measurement setup (**b**) FEMM Simulation contour plot. An experiment was then conducted with the research apparatus; a U-shaped tube was designed and made out of glass (Figures 4 and 5). With the experimental apparatus model as shown in Figure 4, the volume of air trapped in the channel between MRFs and transducer is 1079.375 mm3. The control variable of this study was the direct current (DC) supply, with a voltage of 12 volts and variable currents to generate varying magnetic field strengths for the MRFs.