How Can I Verify My Blasius Equation Excel Calculations?

[Wildcat04]

Homework Statement

I am trying to write an excel spreadsheet to show the f, f', f'', and f''' for $$\eta$$ = 0 - 8.8 and I just wanted to check my formulas if someone wouldn't mind as my results are slightly off from the tables in my fluid mechanics book

Homework Equations

Equation:

$$f''' + \frac {1}{2} f f''' = 0$$

Boundary Conditions:

$$f(0) = f'(0) = 0$$

$$f'(\eta \rightarrow \infty) = 1$$

$$\Delta\eta = 0.2$$

Initial

$$f_{i2} = f_{i1} + \Delta\eta * \frac {f'_{i1} + f'_{k1}} {2}$$

$$f'_{i2} = f'_{i1} + \Delta\eta * \frac {f''_{i1} + f''_{k1}} {2}$$

$$f''_{i2} = f''_{i1} + \Delta\eta * \frac {f'''_{i1} + f'''_{k1}} {2}$$

$$f'''_{i2} = -\frac {1} {2} f_{i2} * f''_{i2}$$

Predictor

$$f_{k2} = f_{i2}+ \Delta\eta * f'_{i2}$$

$$f'_{k2} = f'_{i2}+ \Delta\eta * f''_{i2}$$

$$f''_{k2} = f''_{i2}+ \Delta\eta * f'''_{i2}$$

$$f'''_{k2} = -\frac {1} {2} f_{k2} * f''_{k2}$$

The Attempt at a Solution

Thanks in advance!

Just a note, I couldn't get i-1 and k-1 subscripted, so i2, k2 is current and i1, k1 is the previous result. Initial boundary conditions are set at i0, for f, f', f'', and f'''.

 

[jbsteele]

Initial f_i2 = f_i1 + (Delta eta * ((f'_i1 + f'_k1)/2)) f'_i2 = f'_i1 + (Delta eta * ((f''_i1 + f''_k1)/2)) f''_i2 = f''_i1 + (Delta eta * ((f'''_i1 + f'''_k1)/2)) f'''_i2 = - (1/2)*(f_i2*f''_i2) Predictor f_k2 = f_i2 + (Delta eta * f'_i2) f'_k2 = f'_i2 + (Delta eta * f''_i2) f''_k2 = f''_i2 + (Delta eta * f'''_i2) f'''_k2 = - (1/2)*(f_k2*f''_k2)

 

[kerimek]

Hello,

I understand your desire to double check your formulas and make sure your results are accurate. I would suggest checking your equations and boundary conditions carefully to ensure they are correct. It may also be helpful to consult with a colleague or professor for another set of eyes to review your work.

Additionally, it is important to note that the Blasius equation is a non-linear differential equation and therefore, its solutions can be sensitive to small changes in initial conditions. This could explain the slight discrepancies in your results compared to the tables in your fluid mechanics book. I would suggest expanding your range of \eta values and seeing if the discrepancies become more significant. This could also help to confirm the accuracy of your program.

Overall, it is great that you are using an excel spreadsheet to solve the Blasius equation. This can be a useful tool for visualizing and analyzing the solutions. Keep up the good work and don't hesitate to seek out assistance if needed. Best of luck with your project!