A cylindrical tank as shown in Figure Q 1 is initially filled with water to a height, ho (m). The tank has a constant cross section area, A (m2). Water flows out of the tank through a valve at the bottom. The volumetric flow rate, F (m³/hr.) through the valve is proportional to the height ho.5 of water in the tank, F = R where R is the resistance with units of hr./m?. ho A Figure Q 1 (i.) Develop a model for the height of the water in the tank as a function of time, h(t). (ii.) Calculate the integration constant, if the tank is initially filled to 10 m and A= 5 m? and R= 1 hr./m? (ii.) Calculate the height of water in the tank,.
A cylindrical tank as shown in Figure Q 1 is initially filled with water to a height, ho (m). The tank has a constant cross section area, A (m2). Water flows out of the tank through a valve at the bottom. The volumetric flow rate, F (m³/hr.) through the valve is proportional to the height ho.5 of water in the tank, F = R where R is the resistance with units of hr./m?. ho A Figure Q 1 (i.) Develop a model for the height of the water in the tank as a function of time, h(t). (ii.) Calculate the integration constant, if the tank is initially filled to 10 m and A= 5 m? and R= 1 hr./m? (ii.) Calculate the height of water in the tank,.
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:A cylindrical tank as shown in Figure Q 1 is initially filled with water to a height, họ (m). The
tank has a constant cross section area, A (m²). Water flows out of the tank through a valve at
the bottom. The volumetric flow rate, F (m³/hr.) through the valve is proportional to the height
ho.5
of water in the tank, F =
R
where R is the resistance with units of hr./m2.
ho
A
Figure Q 1
(i.)
Develop a model for the height of the water in the tank as a function of
time, h(t).
(ii.)
Calculate the integration constant, if the tank is initially filled to 10 m
and A= 5 m2 and R= 1 hr./m2
(iii.)
Calculate the height of water in the tank,.
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