Plotting Log as part of an equation in mathematica

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SUMMARY

This discussion focuses on plotting logarithmic functions in Mathematica, specifically using the equation y = 25x / log10(x) - 50x. The user aims to manipulate variables to adjust the steepness of the curve, drawing parallels to a well discharge formula represented as Q = 2π K (Db - Dm) (Dw - Dm) / ln(Ri/Rw). The conversation highlights the importance of understanding both base 10 and natural logarithms in the context of graphical representation and hydraulic modeling.

PREREQUISITES
  • Familiarity with Mathematica 12.0 plotting functions
  • Understanding of logarithmic functions, specifically log10 and natural logarithm (ln)
  • Basic knowledge of hydraulic modeling concepts
  • Ability to manipulate mathematical equations and variables
NEXT STEPS
  • Explore advanced plotting techniques in Mathematica for dynamic variable manipulation
  • Learn about hydraulic conductivity and its impact on well discharge calculations
  • Investigate the effects of different logarithmic bases on curve behavior
  • Study the relationship between porosity, discharge, and curve steepness in groundwater modeling
USEFUL FOR

Mathematics students, hydrologists, engineers, and anyone interested in modeling logarithmic functions and hydraulic systems using Mathematica.

nimbus2506
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Hello I'm trying to plot log as part of an equation in mathematica and it does not seem to be working for me.

for example I'm using Plot y = 25x / log10 (x) - 50x

I'm just experimenting with different numbers and formulas to see what happens to the log curve.

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What I'm doing in more detail, is that I want to be able to change variables so that the curve can become steeper or shallower. I want to introduce about 4 or 5 different variables to control it.

http://en.wikipedia.org/wiki/File:WellHead.gif

I want to try and mimic and simplify this formula to produce the graph above. Where the water table level is controlled by the porosity of the rock and the flow of the well. Low porosity and low discharge from the well result in a steep curve and vise versa.

Q = 2π K (Db - Dm) (Dw - Dm) / ln (Ri/Rw)

where Q = safe well discharge - i.e. the steady state discharge at which no overdraught or groundwater depletion occurs - (m3/day), K = uniform hydraulic conductivity of the soil (m/day), D = depth below soil surface, Db = depth of the bottom of the well equal to the depth of the impermeable base (m), Dm = depth of the watertable midway between the wells (m), Dw is the depth of the water level inside the well (m), Ri = radius of influence of the well (m), Rw=radius of the well (m), ln = natural logarithm, and π = the number pi.

The radius of influence of the wells depends on the pattern of the well field, which may be triangular, square, or rectangular. It can be found as:

Ri = sqrt (At/πN)

http://en.wikipedia.org/wiki/Well_drainage
 
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For base 10 log

Plot[25x / Log[10,x] - 50x,{x,1,100}]

For natural log

Plot[2π K (Db - Dm) (Dw - Dm) / Log[Ri/Rw],{something,somethingelse,somethingother}]