| Name: | Oneeq9 - Pressure drop in a converging diverging nozzle | ||
| Source: | Carnahan, B., Luther, H. A. and Wilkes, J. O., 1969, Applied Numerical Methods, | ||
| Wiley, New York | |||
| Reference/s | Shacham, M. 1989, Chem. Engng. Sci., 44(7), 1495 | ||
| Model: | 1 implicit equation, indep. variable name: P | ||
| Lower difficulty level | |||
| Constraints: P>=0 | |||
| Discontinuities: function undefined for P<0 | |||
| Initial range: Pmin=1, Pmax=100 | |||
| Solved by | Shacham, M., POLYMATH 5.1, build 19, Nov. 17, 2000 | ||
| Model Eqs. | Pressure drop in a converging diverging nozzle |POLVER05_1 | ||
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f(P) = ((gama+1)/2)^((gama+1)/(gama-1))*(2/(gama-1))*((P/Pd)^(2/gama) -(P/Pd)^((gama+1)/gama))-At^2/A^2 # |
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| At = 0.1 # | |||
| A = 0.12 # | |||
| gama = 1.41 # | |||
| Pd = 100 # | |||
| P(min)=1, P(max)=100 | |||
| Variable/function values | Variable | Value | f(x) |
| P | 50.5 |
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| Root 1 | Variable | Value | f(x) |
| P |
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| Root 2 | Variable | Value | f(x) |
| P |
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| Additional information | f'(P)=0 at P=52.66. Derivative based methods may have difficulty | ||
| converging from the vicinity of this point. Multiple roots may | |||
| be overlooked if no proper solution method is used. | |||
| Function plot | |||