Question: A theoretical force balance for the control valve shown in Figure can be expressed as Assuming the second-order differential equation is linear, find values of

A theoretical force balance for the control valve shown in Figure can be expressed as dx_ M d?x PAp + MA - Kx - PrAp -R &e Assuming the second-order differential equation is linear, find values of the coefficients of the equation (in deviation variable form) and determine whether the valve dynamic behavior is overdamped orunderdamped.

dx_ M d?x PAp + MA - Kx - PrAp -R &e dr? where M = mass of movable stem = 10 lbm P= valve air pressure input AD - diaphragm area g, &e = gravity, conversion constants K = spring constant = 3600 lb/ft Pr = fluid pressure Ap = valve plug area R= coefficient of friction (stem to packing) = 15,000 Ib/ft/s %23 x = valve position

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