A pipe carries water at a velocity u. A faulty valve introduces a reactive chemical into...

  

Transcribed Image Text:

A pipe carries water at a velocity u. A faulty valve introduces a reactive chemical into the pipe half-way along its length at a rate of 0.01 kg/s. The chemical is subsequently broken down at a rate proportional to its concentration o (mass of chemical per unit mass of water), this rate amounting to -Yo per meter, where Y=0.5 kg/ms. 0 = 0 X= 0 dx point source A = 0.01 m2 (cross-section area) L = 1 m (length of the pipe) p = 1000 kg/m ( density of water) T= 0.1 kg/ms (Diffusivity of the chemical in water) u (flow velocity) Write a code (Fortran, Matlab, etc..) which uses finite volume method to estimate the concentration o along the pipe. To solve set of Algebraic equations use Thomas Algorithm (TDMA). 1) u= 0.1 m/s, use following differencing schemes for convection. Compare the results with analytical solution. Show the effect of the cell numbers for all schemes. a. Central b. Upwind Hybrid d. QUICK C. 2) u= 2.5 m/s, use following differencing schemes for convection. Compare the results with analytical solution. Show the effect of the cell numbers for all schemes. a. Central b. Upwind c. Hybrid d. QUICK Maximum 4 students are allowable per group. Final Report will be submitted in pdf format (Deadline 06/01/2017) Codes have to be shared in *.f90, *.m, *.cpp, etc (e-mail : byagiz@aselsan.com.tr) The two-part analytical solution is; 4= Eel+ Fel o = Ge He where ki, ki are 21 r And the constants E, F, G, H fixed by the boundary conditions and conditions at x= % are ke -kge? Spt k-kkgek -kgek ra E= -F- kye 4- Sut Hint: For example, if you use 7 cells; loss - por metre =0 dx 1 3 4 6 S= 0.01 kgis Source sowrev- S -0,A-h, +, al t whete b,-0.01(cell 4). 1,=yAr-0.071 2. A pipe carries water at a velocity u. A faulty valve introduces a reactive chemical into the pipe half-way along its length at a rate of 0.01 kg/s. The chemical is subsequently broken down at a rate proportional to its concentration o (mass of chemical per unit mass of water), this rate amounting to -Yo per meter, where Y=0.5 kg/ms. 0 = 0 X= 0 dx point source A = 0.01 m2 (cross-section area) L = 1 m (length of the pipe) p = 1000 kg/m ( density of water) T= 0.1 kg/ms (Diffusivity of the chemical in water) u (flow velocity) Write a code (Fortran, Matlab, etc..) which uses finite volume method to estimate the concentration o along the pipe. To solve set of Algebraic equations use Thomas Algorithm (TDMA). 1) u= 0.1 m/s, use following differencing schemes for convection. Compare the results with analytical solution. Show the effect of the cell numbers for all schemes. a. Central b. Upwind Hybrid d. QUICK C. 2) u= 2.5 m/s, use following differencing schemes for convection. Compare the results with analytical solution. Show the effect of the cell numbers for all schemes. a. Central b. Upwind c. Hybrid d. QUICK Maximum 4 students are allowable per group. Final Report will be submitted in pdf format (Deadline 06/01/2017) Codes have to be shared in *.f90, *.m, *.cpp, etc (e-mail : byagiz@aselsan.com.tr) The two-part analytical solution is; 4= Eel+ Fel o = Ge He where ki, ki are 21 r And the constants E, F, G, H fixed by the boundary conditions and conditions at x= % are ke -kge? Spt k-kkgek -kgek ra E= -F- kye 4- Sut Hint: For example, if you use 7 cells; loss - por metre =0 dx 1 3 4 6 S= 0.01 kgis Source sowrev- S -0,A-h, +, al t whete b,-0.01(cell 4). 1,=yAr-0.071 2.

Answer rating: 100% (QA)

Solution Given il Velocty hate longts a 001 kgs u Y 2 ... View the full answer