The inside of a container is an ellipsoid (as shown) 2 2 (²) ³² + ( )² + (²) ²³ = 1 ree holes are made (one at the south pole, and one at the equator, for leaking, one Z at the north pole for air intake) to enable the same draining constant k for the leaking holes. The draining process follows the IVP A(h)dh = -k√h dt
The inside of a container is an ellipsoid (as shown) 2 2 (²) ³² + ( )² + (²) ²³ = 1 ree holes are made (one at the south pole, and one at the equator, for leaking, one Z at the north pole for air intake) to enable the same draining constant k for the leaking holes. The draining process follows the IVP A(h)dh = -k√h dt
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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Three holes are made (one at the south pole, and one at the equator, for leaking, one
at the north pole for air intake) to enable the same
draining constant k for the leaking holes. The
draining process follows the IVP
A(h)dh
-k√h
Z
The inside of a container is an ellipsoid (as shown)
2
2
(²) ² + (²)² + (²³)² =
b
1
h
=
dt
h(t = 0) = ho
y
introduced by Torricelli in 1643. In the DE, A (h) is
the cross-section area at the height (from the
leaking point) h.
Derive the formula for the time needed to empty a
fully filled tank.
Note: Both leaking holes are at work while draining the upper half tank and, naturally, only one hole
leaks while draining the lower half.
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