If water is drained from a vertical cylindrical tank by opening a valve at the base, the water will flow fast when the tank is full and slow down as it continues to drain. As it turns out, the rate at which the water level drops is: dy dt : -ky0.5 = where k is a constant depending on the shape of the hole and the cross-sectional area of the tank and drain hole. The depth of the water y is measured in meters and the time t in minutes. If k = 0.06, determine how long it takes the tank to drain if the fluid level is initially 3 m. Solve by applying Euler's Method or 4th Order Runge-Kutta (RK4) Method with your choice of At.
If water is drained from a vertical cylindrical tank by opening a valve at the base, the water will flow fast when the tank is full and slow down as it continues to drain. As it turns out, the rate at which the water level drops is: dy dt : -ky0.5 = where k is a constant depending on the shape of the hole and the cross-sectional area of the tank and drain hole. The depth of the water y is measured in meters and the time t in minutes. If k = 0.06, determine how long it takes the tank to drain if the fluid level is initially 3 m. Solve by applying Euler's Method or 4th Order Runge-Kutta (RK4) Method with your choice of At.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:If water is drained from a vertical cylindrical tank by opening a valve at the base, the water
will flow fast when the tank is full and slow down as it continues to drain. As it turns out, the
rate at which the water level drops is:
dy
dt
=
-ky⁰.5
where k is a constant depending on the shape of the hole and the cross-sectional
area of the tank and drain hole. The depth of the water y is measured in meters
and the time t in minutes. If k = 0.06, determine how long it takes the tank to
drain if the fluid level is initially 3 m. Solve by applying Euler's Method or 4th
Order Runge-Kutta (RK4) Method with your choice of At.
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