Water flows in a little tank, which has a leak. At the moment t=0 the tank is empty. The volume of the tank is Vcm3 at the moment (t) minutes. Water flows in the tank at a flow of 80m3 per minute. Due to the leak water leak out of the tank with a flow of kV cm3 per minute where k is a positive constant. (i) By using a differential equation show that: V=1/k (A-Ae-kt) where A is a real positive a to be determinate. (ii) Determinate the value of k when t=15 and V=500
Water flows in a little tank, which has a leak. At the moment t=0 the tank is empty. The volume of the tank is Vcm3 at the moment (t) minutes. Water flows in the tank at a flow of 80m3 per minute. Due to the leak water leak out of the tank with a flow of kV cm3 per minute where k is a positive constant. (i) By using a differential equation show that: V=1/k (A-Ae-kt) where A is a real positive a to be determinate. (ii) Determinate the value of k when t=15 and V=500
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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Water flows in a little tank, which has a leak. At the moment t=0 the tank is empty. The volume of the tank is Vcm3 at the moment (t) minutes. Water flows in the tank at a flow of 80m3 per minute. Due to the leak water leak out of the tank with a flow of kV cm3 per minute where k is a positive constant.
(i) By using a differential equation show that: V=1/k (A-Ae-kt) where A is a real positive a to be determinate.
(ii) Determinate the value of k when t=15 and V=500
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