Develop a mathematical model of the pressure p in the container.

 

Dry air at a constant temperature of 25°C passes through a valve out of a rigid cubic container of 1.5 m on each side (Figure 7.42). The pressure po at the outlet of the valve is constant, and it is less than p. The valve resistance is approximately linear, and

= 1000 Pa・s/kg. Assume that the process is isothermal.

a. Develop a mathematical model of the pressure in the container.

b. Construct a Simulink block diagram to find the output p(t) of the pneumatic system if the pressure inside the container is initially 2 atm and the pressure at the outlet is 1 atm.

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erive the differential equations in terms of the liquid heights h1 and h2.

  Figure 7.18 shows a liquid-level system in which two tanks have cross-sectional areas A1 and A2, respectively. The volume flow rate into tank 1 is qi. A pump is connected to the bottom….

Derive the differential equation relating the liquid height h and the volume flow rate qi at the inlet.

  Consider the single-tank liquid-level system shown in Figure 7.19, where the volume flow rate into the tank through a pipe is qi. The liquid leaves the tank through an orifice….

Derive the differential equations in terms of the liquid heights h1 and h2.

Figure 7.20 shows a hydraulic system of two interconnected tanks that have the same cross-sectional area of A. A pump is connected to tank 1. Assume that the relationship between the….