Solution Found!
A theoretical force balance for the control valve shown in
Chapter 9, Problem 9.7(choose chapter or problem)
A theoretical force balance for the control valve shown in Fig. 9.7 can be expressed as g dx M d2x PAn+ M- -Kx -P1A -R- =-- gc P dt gc d? where M = mass of movable stem = 10 lbm P = valve air pressure input An = diaphragm area g, gc = gravity, conversion constants K = spring constant = 3,600 lbf/ft Pr = fluid pressure Ap = valve plug area R = coefficient of friction (stem to packing) = 15,000 lbf/ft/s x = valve position 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 or underdamped.
Questions & Answers
QUESTION:
A theoretical force balance for the control valve shown in Fig. 9.7 can be expressed as g dx M d2x PAn+ M- -Kx -P1A -R- =-- gc P dt gc d? where M = mass of movable stem = 10 lbm P = valve air pressure input An = diaphragm area g, gc = gravity, conversion constants K = spring constant = 3,600 lbf/ft Pr = fluid pressure Ap = valve plug area R = coefficient of friction (stem to packing) = 15,000 lbf/ft/s x = valve position 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 or underdamped.
ANSWER:Step 1 of 4
The given details are:
M = mass of movable stem = 
K = spring constant =
R = coefficient of friction (stem to packing) = 