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 of area Ao. Denote Cd as the discharge coefficient, which is the ratio of the actual mass flow rate to the theoretical one, and lies in the range of 0 <>Cd <>1 because of friction effects. Derive the differential equation relating the liquid height and the volume flow rate qi at the inlet. The tank’s cross-sectional area is constant. The density ρ of the liquid is constant.

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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 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….

Determine the heat flow rate through the wall.

Consider heat transfer through an insulated frame wall of a house. The thermal conductivity of the wall is 0.055 W/(m・°C). The wall is 0.15 m thick and has an area….