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Q1. A basic flapper/nozzle device is shown in Fig Q8. The pneumatic signal for the input bellows unit is proportional to the measured temperature within the range 0-150℃. The output signal range is to be 20-100 kN/m². The characteristic of the input bellows is 4 mm/℃, and the characteristic of the nozzle is 0.2 kN/m² per mm of flapper movement. Calculate EACH of the following:

(a) The flapper movement at the nozzle for 100% input change;

(b) The resulting change in output;

(c) The gain of the device;

(d) The new setting of x, the distance from the pivot to the nozzle, to achieve a gain of 0.5;

(e) The output pressure at 85℃ with a gain of 0.5 if the output pressure was 50 kN/m² at a temperature of 55℃.