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4.8 A surge tank in Fig. E4.8 is designed with a slotted weir so that the outflow rate, w, isproportional to the liquid level to the 1.5 power, that is,wRh15where R is constant. If the single stream enters the tank with flow rate w, find the transferfunction H(s)/W(s). Identify the gain and all time constants. Verify unitsThe cross-sectional area of the tank is A. Density ρ is constant.-WeirFigure E4.8

Question
4.8 A surge tank in Fig. E4.8 is designed with a slotted weir so that the outflow rate, w, is
proportional to the liquid level to the 1.5 power, that is,
wRh15
where R is constant. If the single stream enters the tank with flow rate w, find the transfer
function H(s)/W(s). Identify the gain and all time constants. Verify units
The cross-sectional area of the tank is A. Density ρ is constant.
-Weir
Figure E4.8
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4.8 A surge tank in Fig. E4.8 is designed with a slotted weir so that the outflow rate, w, is proportional to the liquid level to the 1.5 power, that is, wRh15 where R is constant. If the single stream enters the tank with flow rate w, find the transfer function H(s)/W(s). Identify the gain and all time constants. Verify units The cross-sectional area of the tank is A. Density ρ is constant. -Weir Figure E4.8

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Step 1

Apply material balance on the given system as:

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Step 2

Use Tylor series to expand the equation (1) as shown below.

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Step 3

Now, take Laplace transform of equation (2) and r...

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