Nonlinear Equation Solution
| Variable | Value | f(x) | Initial value | Initial f(x) | |
|---|---|---|---|---|---|
| 1 | vt | 0.015781618 | -9.6e-9 | 0.04965 | 2.1e+1 |
| 2 | rho | 994.6 | 994.6 | ||
| 3 | g | 9.80665 | 9.807 | ||
| 4 | rhop | 1800 | 1800 | ||
| 5 | Dp | 0.000208 | 0.000208 | ||
| 6 | vis | 0.0008931 | 0.0008931 | ||
| 7 | Re | 3.6556385 | 11.5 | ||
| 8 | CD | 8.8426583 | 3.701 |
Root Finding Plot
Settings and Hints
| Name/Source | Value | Type | |
|---|---|---|---|
| 1 | Number of equations | 8 | Setting |
| 2 | Implicit equations | 1 | Setting |
| 3 | Explicit equations | 7 | Setting |
| 4 | Elapsed time | 0.000 ms | Setting |
| 5 | Solution method | Brent | Setting |
| 6 | Tolerance F | 1e-7 | Setting |
| 7 | Max iterations | 150 | Setting |
| 8 | #@chart_size = 428,300 | Default (array) | |
| 9 | #@report_fix_digits = 8 | Default (integer) | |
| 10 | #@report_show_source = true | Default (boolean) | |
| 11 | #@report_show_header = false | Default (boolean) | |
| 12 | #@report_show_charts = true | Default (boolean) | |
| 13 | #@report_show_settings = true | Default (boolean) | |
Messages
| Severity | Description | |
|---|---|---|
| 1 | Info | -Infor- Implicit variables (1) vt |
| 2 | Info | -Infor- Explicit variables (7) rho, g, rhop, Dp, vis, Re, CD |
| 3 | Info | -Infor- All variables (8) vt, CD, rho, g, rhop, Dp, vis, Re |
Source
# Terminal Velocity: NLE with 'if' condition
# Verified Solution: vt = 0.015782
# Ref.: Comput. Appl. Eng. Educ. 6: 174, 1998
f(vt) = vt^2*(3*CD*rho)-4*g*(rhop-rho)*Dp
rho = 994.6
g = 9.80665
rhop = 1800
Dp = 0.208e-3
vis = 8.931e-4
Re = Dp*vt*rho/vis
CD = if (Re < 0.1) then (24/Re) else (24*(1+0.14*Re^0.7)/Re)
vt(min) = 0.0001
vt(max) = 0.05
# Verified Solution: vt = 0.015782
# Ref.: Comput. Appl. Eng. Educ. 6: 174, 1998
f(vt) = vt^2*(3*CD*rho)-4*g*(rhop-rho)*Dp
rho = 994.6
g = 9.80665
rhop = 1800
Dp = 0.208e-3
vis = 8.931e-4
Re = Dp*vt*rho/vis
CD = if (Re < 0.1) then (24/Re) else (24*(1+0.14*Re^0.7)/Re)
vt(min) = 0.0001
vt(max) = 0.05