28. Water flows from an inverted conical tank with circular orifice at the rate dx -0.6r² /2g- dt A(x)' where r is the radius of the orifice, æ is the height of the liquid level from the vertex of the cone, and A(x) is the area of the cross section of the tank æ units above the orifice. Supposer = 0.1 ft, g= 32.1 ft/s², and the tank has an initial water level of 8 ft and initial volume of 512(T/3) ft°. Use the Runge-Kutta method of order four to find the following: a. The water level after 10 min with h = 20 s b. When the tank will be empty, to within 1 min

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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28. Water flows from an inverted conical tank with circular
orifice at the rate
dx
-0.6rr² /2g-
A(z)'
dt
where r is the radius of the orifice, æ is the height of the
liquid level from the vertex of the cone, and A(x) is the
area of the cross section of the tank x units above the
orifice. Suppose r = 0.1 ft, g = 32.1 ft/s², and the tank
has an initial water level of 8 ft and initial volume of
512(7/3) ft°. Use the Runge-Kutta method of order four
to find the following:
a. The water level after 10 min with h = 20 s
b. When the tank will be empty, to within 1 min
Transcribed Image Text:28. Water flows from an inverted conical tank with circular orifice at the rate dx -0.6rr² /2g- A(z)' dt where r is the radius of the orifice, æ is the height of the liquid level from the vertex of the cone, and A(x) is the area of the cross section of the tank x units above the orifice. Suppose r = 0.1 ft, g = 32.1 ft/s², and the tank has an initial water level of 8 ft and initial volume of 512(7/3) ft°. Use the Runge-Kutta method of order four to find the following: a. The water level after 10 min with h = 20 s b. When the tank will be empty, to within 1 min
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