Find the temperature of the sphere at any time, as well as its steady-state value.

 

1. Consider a first-order system with time constant τ and zero initial condition. Find the system’s unit-step response for τ =  and  , plot the two curves versus 0 ≤ ≤ 2 in the same graph, and comment.

2. The temperature of a steel sphere with initial temperature Tsubmerged in water

with temperature Tis governed by the initial-value problem RC +  T  = Ti , T(0) = T0

where:

is the thermal resistance due to convection

is the thermal capacitance of the sphere

Find the temperature of the sphere at any time, as well as its steady-state value.

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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.

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