Question

104 AUTOMATIC CONTROL ENGINEERING 3.44 In Fig. P3.44 is shown a speed-sensing device in which the position $x$ is proportional to the angular velocity of the gear pump. The rate of flow $q$ through the pump is proportional to the speed of rotation, $q = C_1\omega$. Because of the fixed orifice, the pressure $p$ is proportional to the rate of flow $q$, $p = C_2q$. The force balance of the bellows-spring combination is $K_s x = Ap$, where $K_s$ is the spring rate and $A$ is the area of the bellows. Determine the equation relating the position $x$ to the speed $\omega$.

          104 AUTOMATIC CONTROL ENGINEERING
3.44 In Fig. P3.44 is shown a speed-sensing device in which the position $x$ is proportional to the
angular velocity of the gear pump. The rate of flow $q$ through the pump is proportional to the speed
of rotation, $q = C_1\omega$. Because of the fixed orifice, the pressure $p$ is proportional to the rate of flow $q$,
$p = C_2q$. The force balance of the bellows-spring combination is $K_s x = Ap$, where $K_s$ is the spring
rate and $A$ is the area of the bellows. Determine the equation relating the position $x$ to the speed $\omega$.

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104 AUTOMATIC CONTROL ENGINEERING
3.44 In Fig. P3.44 is shown a speed-sensing device in which the position x is proportional to the
angular velocity of the gear pump. The rate of flow q through the pump is proportional to the speed
of rotation, q = C1ω. Because of the fixed orifice, the pressure p is proportional to the rate of flow q,
p = C2q. The force balance of the bellows-spring combination is Ks x = Ap, where Ks is the spring
rate and A is the area of the bellows. Determine the equation relating the position x to the speed ω.

Added by Melanie R.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Ethan Deweese

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The position of the speed-sensing device is proportional to the angular velocity of the gear pump. Show more…

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Thanks in advance, it is only a photo I have. I hope it is clear. Please try to read it. I am sorry, but I have this only. Thanks again. IOA-AUTOMATIC CONTROL ENGINEERING In Figure P3.44, shown is a speed-sensing device in which the position is proportional to the angular velocity of the gear pump. The rate of flow through the pump is proportional to the speed of rotation. Because of the fixed orifice, the pressure is proportional to the rate of flow. The force balance of the bellows-spring combination is Ax - Ap, where K is the spring rate and A is the area of the bellows. Determine the equation relating the position to the speed. Governor spring Bellows Fixed orifice P Gear pump Figure P3.44

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