Considering the system in the figure, to which two flows w1(t) and w2(t) enter, we have an exit flow w3(t)= CvAs2gh (t) m^3/min.The tank is a cylinder 2.5 m high and 2 m in diameter, the liquid has a density of 1000 kg/m^3, orifice constant Cv=4.3, orifice diameter 10 in. The normal operating procedure is to fill the tank until it reaches its steady state height of 1.75 m using a constant flow of w1=0.000170 m^3/min and a flow w2 in m^3/min.

1) report the value of w2 necessary for the system to stabilize at a height of 1.75 m, considering only w1, w2 and w3.

2) Find the transfer functions H(s)/W1(s) and H(s)/W2(s) 3) One day a hole was opened at a height of 1 m in the tank due to corrosion problems, producing a leak that can be approximated using the following equation: 

q4=0.016(h-1)

Suppose that when the hole is opened the system was filled to a height of 1.75 m, i.e. h(0)=1.75 m 4) If the system normally operates with a height of 1.75m, select this value as the linearization point and find the transfer functions H(s)/W1(s) and H(s)/W2(s), considering in the model to the hole, substitute all system parameters into the transfer functions 

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