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a. Write the equation ofrotational motion at motor's output shaft. b. Write the equation of motion for the rotational motion of the load cylinder. c. Write the equation of motion for the vertical motion of the blocking mass, neglecting drag force of water in the pipe. d. Write the equations describing changes in the level of the pool. Assume the change in inflow rate to the pool is related to vertical motion of the blocking mass by: q,(r) = Bx(r) with B=1m2/sec

a. Write the equation ofrotational motion at motor's output shaft. b. Write the equation of motion for the rotational motion of the load cylinder. c. Write the equation of motion for the vertical motion of the blocking mass, neglecting drag force of water in the pipe. d. Write the equations describing changes in the level of the pool. Assume the change in inflow rate to the pool is related to vertical motion of the blocking mass by: q,(r) = Bx(r) with B=1m2/sec

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Question
a. Write the equation ofrotational motion at motor's output shaft.
b. Write the equation of motion for the rotational motion of the load cylinder.
c. Write the equation of motion for the vertical motion of the blocking mass, neglecting drag
force of water in the pipe.
d. Write the equations describing changes in the level of the pool. Assume the change in inflow
rate to the pool is related to vertical motion of the blocking mass by:
q,(r) = Bx(r) with B=1m2/sec
Motor i(1) Central Water Ost Source x(1) Q +q,(1) H + h(t) Рool R Q +q,1) C Variable Value&Unit Description Variable Value&Unit Description Coefficient of linear spring i(t) Input motor current 1.5 N/m A Vertical Inertia of motor's 3.5 kgm x() position of the | blocking mass Mass of the rotor Motor's damping coefficient bu 0.25 Nms/rad M 1kg blocking mass Steady-state water flow rate Steady-state K, 25 Nm/ A Motor torque constant m'/s Angular position of rad motor shaft head of tank Change in inflow from central source Change in flow from water tank: to pool Change in head of pool Resistance of Coefficient of rotational spring 9.(0) m/s ka 0.5 Nm/rad 0.5 kgm Inertia of load m*/s 0.25m Radius of load h(t) 0,(4) Angular position of load 0.1s/m² rad R valve Coefficient of linear Capacitance of b. 0.5 Ns/m C 0.015m damper water tank
Transcribed Image Text:Motor i(1) Central Water Ost Source x(1) Q +q,(1) H + h(t) Рool R Q +q,1) C Variable Value&Unit Description Variable Value&Unit Description Coefficient of linear spring i(t) Input motor current 1.5 N/m A Vertical Inertia of motor's 3.5 kgm x() position of the | blocking mass Mass of the rotor Motor's damping coefficient bu 0.25 Nms/rad M 1kg blocking mass Steady-state water flow rate Steady-state K, 25 Nm/ A Motor torque constant m'/s Angular position of rad motor shaft head of tank Change in inflow from central source Change in flow from water tank: to pool Change in head of pool Resistance of Coefficient of rotational spring 9.(0) m/s ka 0.5 Nm/rad 0.5 kgm Inertia of load m*/s 0.25m Radius of load h(t) 0,(4) Angular position of load 0.1s/m² rad R valve Coefficient of linear Capacitance of b. 0.5 Ns/m C 0.015m damper water tank
PROBLEM STATEMENT The figure illustrates water flow from a central water source to a pool. Motor's motion due to input current is transmitted to the load cylinder via the rotational spring, and the rope is winded to this cylinder as shown. The flow of the water from the central water source is controlled by the vertical motion of the blocking mass inside the pipe. At steady-state, the volumetric outflow rate and head of the pool are O and H, respectively. When a small change, h, occurs in the head of the pool, the flow rates change by q, and 9, as shown. PROBLEMS 1) Assuming that all quantities are measured from their steady-state values, develop a mathematical model of the system using the following steps. Assume that the central water source is much larger than the pool so that there will be water in it for all future times. a. Write the equation of rotational motion at motor's output shaft. b. Write the equation of motion for the rotational motion of the load cylinder. c. Write the equation of motion for the vertical motion of the blocking mass, neglecting drag force of water in the pipe. d. Write the equations describing changes in the level of the pool. Assume the change in inflow rate to the pool is related to vertical motion of the blocking mass by: 9.(t) = Bx(t) with ß=1m² /sec
Transcribed Image Text:PROBLEM STATEMENT The figure illustrates water flow from a central water source to a pool. Motor's motion due to input current is transmitted to the load cylinder via the rotational spring, and the rope is winded to this cylinder as shown. The flow of the water from the central water source is controlled by the vertical motion of the blocking mass inside the pipe. At steady-state, the volumetric outflow rate and head of the pool are O and H, respectively. When a small change, h, occurs in the head of the pool, the flow rates change by q, and 9, as shown. PROBLEMS 1) Assuming that all quantities are measured from their steady-state values, develop a mathematical model of the system using the following steps. Assume that the central water source is much larger than the pool so that there will be water in it for all future times. a. Write the equation of rotational motion at motor's output shaft. b. Write the equation of motion for the rotational motion of the load cylinder. c. Write the equation of motion for the vertical motion of the blocking mass, neglecting drag force of water in the pipe. d. Write the equations describing changes in the level of the pool. Assume the change in inflow rate to the pool is related to vertical motion of the blocking mass by: 9.(t) = Bx(t) with ß=1m² /sec
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