A tank shaped like a vertical cylinder initially contains water to a depth of 9m. The bottom plug is pulled at time t = 0. After 1h, the depth has dropped to 4m. The water to drain from the tank if the rate of change of depth of water in the cylinder, y, is described by: dy -k√y where y is the depth of the water in the cylinder (m) t is the time (hr) k is a constant The differential equation in the above can be derived using the Bernouli Equation and the Mass Continuity Equation. Bernouli Equation: P/p+ 0.5v² + gz=0 Mass Continuity Equation Mass in - Mass out+ Generation - Consumption = accumulation. dy dt = 1) derive the differential equation equation 2) express k in terms of the properties of the system. -k√y using the Bernoulli equation and mass continuity
A tank shaped like a vertical cylinder initially contains water to a depth of 9m. The bottom plug is pulled at time t = 0. After 1h, the depth has dropped to 4m. The water to drain from the tank if the rate of change of depth of water in the cylinder, y, is described by: dy -k√y where y is the depth of the water in the cylinder (m) t is the time (hr) k is a constant The differential equation in the above can be derived using the Bernouli Equation and the Mass Continuity Equation. Bernouli Equation: P/p+ 0.5v² + gz=0 Mass Continuity Equation Mass in - Mass out+ Generation - Consumption = accumulation. dy dt = 1) derive the differential equation equation 2) express k in terms of the properties of the system. -k√y using the Bernoulli equation and mass continuity
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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Can someone help me with what does "express k in terms of the parameters of the system" and how to do it?
Transcribed Image Text:A tank shaped like a vertical cylinder initially contains water to a depth of 9m. The
bottom plug is pulled at time t = 0. After 1h, the depth has dropped to 4m.
The water to drain from the tank if the rate of change of depth of water in the
cylinder, y, is described by:
where
y is the depth of the water in the cylinder (m)
t is the time (hr)
k is a constant
=-k√y
The differential equation in the above can be derived using the Bernouli Equation and the Mass
Continuity Equation.
Bernouli Equation:
P/p+0.5v² + gz=0
Mass Continuity Equation
Mass in - Mass out + Generation - Consumption = accumulation.
dy
dt
1) derive the differential equation
equation
2) express k in terms of the properties of the system.
=
-k√y using the Bernoulli equation and mass continuity
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