Oneeq9

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

EXCEL FILE  

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 #

TEXT FILE  

At = 0.1 #

POLYMATH FILE 

A = 0.12 #
  gama = 1.41 #
  Pd = 100 #
  P(min)=1, P(max)=100
       
Variable/function values Variable Value f(x)
  P 50.5

3.0352E-01
       
Root 1 Variable Value f(x)
  P

25.743977294088

-2.2204E-16
       
Root 2 Variable Value f(x)
  P

78.905412035983

-2.6645E-15
       
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