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  3. problem 1 figure 1 shows a twotank hydraulic system the...

Question: problem 1 figure 1 shows a twotank hydraulic system the...

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Problem 1. Figure 1 shows a two-tank hydraulic system. The pump takes water from the sump (reservoir) at atmospheric pressure Pm and increases the pressure by the constant amount ΔΡ--f)gh, where H is the pressure head. Assume that the constant pressure head H is greater than the vertical-wall height of tank 1. Flow through all valves is laminar. (a) Derive the complete mathematical model with tank pressures P1 and P2 as the dynamic variables and head H as the input variable (b) Introduce the gage pressure P.PPatm and P2P2 Patm as dynamic variables, and rewrite the mathematical models obtained in (a) in tems of P and .2respectively (c) Write the linear system of equations that model the complete fluid systems (d) Write the linear system of equation in matrix fornm PR.2(5) H(s) (e) Derive the mathematical equation of the transfer function Tank 1 Tank 2 Base pressure, P Base pressure, P Pump Area, A Area, A 0 Valve, R Valve, R Valve, R Sump (reservoir) Fig. 1. Two-tank hydraulic system
Problem 4. A hydraulic damper or dashpot device is shown in Fig.4. The cylinder is rigidly fixed and the rod and piston have mass . The displacement of the piston x is measured from the center location of the cylinder, and Vo is the cylinder volume when x-0 (e.g., Vi V2-Voif r0). Several orifices allow hydraulic fluid to flow between chambers 1 and 2 and their total area is Ao. Friction between the piston and cylinder is assumed to be linear and is modeled by viscous friction coefficient h. Derive the complete mathematical model of the damper device for two cases (a) The fluid is assumed to be incompressible, and therefore flow rate in/out of a chamber is always equal to the time-rate of volume or Q differential between chambers is a function of velocity ]. A. [Hint: the pressure (b) The fluid is assumed to be compressible, and therefore we cannot assume that QAalways holds. The pressure time-rate equation must be included in the model Both models must accommodate positive and negative velocity Area, AArea, A Rigid connection Applied force, F Rod +Piston Chamber 1 mass, m Chamber 2 Orifices otal area-A Viscous friction, Fig.4. Hydraulic damper system
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