Oneeq15b

Name: Oneeq15b - Sinkage depth of sphere in water - 2nd form

Source:

Reference/s Shacham, M. 1989, Chem. Engng. Sci., 44(7), 1495

Model: 1 implicit equation, indep. variable name: h

higher difficulty level

Constraints: h>0, h<2

Discontinuities: function undefined at h=0 and h=3

Initial range: hmin=-2, hmax=5

Solved by Shacham, M., POLYMATH 5.1, build 19, Dec 12, 2001

Model Eqs. Sinkage depth of sphere in water - 2nd form|POLVER05_1

EXCEL FILE
f(h) = 2.4/(h*(3-h))-h #

TEXT FILE
h(min)=-2, h(max)=5

POLYMATH FILE

Variable/function values Variable Value f(x)

h 1.5 -4.3333E-01

Variable Value f(x)

Root1 h -0.795219745444464 -5.5511E-16

Root2 h 1.134137843811 -2.2204E-16

Root3 h 2.66108190354552 8.8818E-16

Additional information The radius of convergence of derivative based methods can be

very small in the vicinity of the only physically correct root (h=1.134)

because f'(h)=0 at h=2.173 and the functin goes to infinity near h=0

and h=3

Function plot

Name:	Oneeq15b - Sinkage depth of sphere in water - 2nd form
Source:

Reference/s	Shacham, M. 1989, Chem. Engng. Sci., 44(7), 1495

Model:	1 implicit equation, indep. variable name: h
	higher difficulty level
	Constraints: h>0, h<2
	Discontinuities: function undefined at h=0 and h=3
	Initial range: hmin=-2, hmax=5

Solved by	Shacham, M., POLYMATH 5.1, build 19, Dec 12, 2001

Model Eqs.	Sinkage depth of sphere in water - 2nd form\|POLVER05_1
EXCEL FILE	f(h) = 2.4/(h*(3-h))-h #
TEXT FILE	h(min)=-2, h(max)=5
POLYMATH FILE
Variable/function values	Variable	Value	f(x)
	h	1.5	-4.3333E-01

	Variable	Value	f(x)
Root1	h	-0.795219745444464	-5.5511E-16
Root2	h	1.134137843811	-2.2204E-16
Root3	h	2.66108190354552	8.8818E-16

Additional information	The radius of convergence of derivative based methods can be
	very small in the vicinity of the only physically correct root (h=1.134)
	because f'(h)=0 at h=2.173 and the functin goes to infinity near h=0
	and h=3
Function plot