Inner Boundary Conditions

Hello Gents,

Q:/ What is the reason for letting the inner boundary condition = (-1) when solving the radial flow of infinite form of diffusivity equation, and I would like to know what would happen if I didn't equate it with (-1).

As in the attached pic: https://i.imgur.com/AVesmHM.png

and here is the original pdf if you want: http://www.pe.tamu.edu/blasingame/da..._DimLssVar.pdf

Stuck finding out the manual solution for finding x in this logarithmic equation

Good day,

I got stuck finding the manual solution for this problem without relying to the solve function of Casio calculator

The original equation was

[(1+x)40] -1 = (181205.95/3000)x

Then I tried using properties of logarithm and I simplified it to this equation:

[ln(181205.95/3000)]/40 = ln(1+x) - (1/40)[ln(x+3000/181205.95)]

0.102526 = ln(x+1) - 0.025ln(x+0.0165557)

Answer: x = 0.02

Fluid mechanics

A hollow sphere 6 in inside diameter is rotated on a cable at 100 rpm. If the cable is 6 ft long and makes an angle of 30 degrees with the horizontal, what is the pressure in the center of the sphere if it is full of water? what is the equivalent specific weight at that point?

Engineering Books:

What are the books with best explanations of the subject matter that are mostly used as reference in the subjects:
-Safety Management
-Circuits Analysis 3
-Mechanics of deformable bodies
-Basic Electronics Engineering
-Advance ENgineering Math
-Dynamics of Rigid Bodies
-Engineering Electromagnetics