# Blasius Equation Program

1. Nov 10, 2009

### Wildcat04

1. The problem statement, all variables and given/known data

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

2. Relevant 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

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

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

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

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

3. The attempt at a solution

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'''.