1A liquid level measurement sensor must be designed for a tank containing water of density pw =1000 kg/m³ using a displacer. The displacer is a solid block of density Pai

=1500 kg/m3 with radius r = 5 cm and height h =50 cm. The displacer is connected to one end of a cantilever beam of length L= 50 cm, width w=10 cm, thickness t=5 mm and Young's modulus E=200 GPa as shown below: Where should a strain gauge be placed on the cantilever? Give reasoning. Assume that when the tank is empty, the displacer is extremely close to the bottom surface of the tank but does not make contact. Calculate the displacement of the cantilever tip and the strain measured by the strain gauge when the tank is empty. (5 marks)Derive the expression for strain measured by the strain gauge when the displacer is submerged by length l in water in the tank. Calculate the strain measured by the strain gauge when the displacer is fully submerged. The strain gauge is a semiconductor strain gauge with gauge factor G=100 and reference resistance of Ro temperature). The strain gauge is connected to a Wheatstone bridge asR1. The resistances R2, R3 and R4 as fixed resistances, where R4=R3. The Wheatstone bridge is balanced when the tank is empty. Determine the values of the three fixed resistors for a bridge with maximum sensitivity.= 100 Q (assume no effect of marks)Using the expression for the output voltage Eth in terms of the bridge resistances (R1, R2, R3 and R4), derive the expression for the sensitivity of the device with respect to the submerged length of the displacer.Calculate the sensitivity of the device in mV/mm, when the tank is completely empty and when the tank is completely full, considering a supply voltage of Vo = 5 V. If you assume the sensitivity of the device with respect to the submerged length to be linear, and deth/dt equal to the sensitivity obtained in e), find the percentage linearity of the device.