Mathcad Project (ChE)

30 San Miguel, John Andre N. 5ChE – A

ACTIVITY 8: MATHCAD PROJECT

Transport Processes Conduction: A furnace consists of 60cm of chrome brick. The brick has a specific heat of 0.4cal/g-°C. The temperature of the inside surface of the wall is 600°C and the outer surface is 200°C. (a) Calculate the thermal diffusivity of the brick (b) What is the thermal conductivity of the brick (c) Calculate the heat loss per hour through a wall 2m high and 2m long Figure:

60c

2

Ti

2 1 T1 = 600°C

2 T2 = 200°C

SOLUTION:

Momentum Transfer Friction Loss in a straight pipe and Effect of type of pipe: A liquid having a density of 801kg/m3 and a viscosity of 1.49x10-3 Pa-s is flowing through a horizontal straight pipe at a velocity of 4.57m/s. The commercial steel pipe is 1 and ½ in. nominal pipe size, schedule 40. For a length of pipe of 61m, (a) Calculate the friction loss FL (b) For a smooth tube of the same inside diameter, calculate the friction loss. What is the percent reduction fo the FL for the smooth tube? Figure Liquid ρ = 801kg/m3 μ = 1.49x103 Pa-s v = 4.57m/s

SOLUTION:

1 1/2 ‘’ Sch 40 Steel Pipe LS = 61m

Heat and Mass Transfer Evaporation: A feed of 4535kg/h of a 2.0wt % salt solution at 311K enter continuously a single-effect evaporator and is being concentrated to 3.0wt%. The evaporation is at atmospheric pressure and the area of the evaporator is 69.7m2. Saturated steam at 383.2K is supplied for heating. Since the solution is dilute, it can be assumed to have the same boiling point as water. The heat capacity of the feed can be taken as Cp = 4.20kJ/kg-K. Calculate the amounts of vaport and liquid product and the overall heat transfer coefficient U. Diagram

E P1 = 1atm =

Sat’d Steam T=

Vo C

4535kg/hr TF = 311K XF = 0.02 CpF = 4.10kJ/kg-K

SOLUTION:

F

L XL= Area =

Separation Processes Extraction: A countercurrent multiple stage contact extraction system is to treat 50tons/hr of wet sliced sugar beets with fresh water as solvent. The beets have the following analysis: Component Water Pulp Sugar

Mass fraction 0.48 0.40 0.12

The strong solution leaving the system is to contain 0.14 mass fraction of sugar and 97% percent of the sugar in the sliced beets is to be recovered. Determine the number of extraction cells required if each ton of dry pulp retains 3 tons of solution, assuming equilibrium between the underflow and the overflow from each cell. Diagram Ya = 0.15 97% recovery

Fresh Vb

V a

a

1

N

b Lb

La = 50tons/hr XAb = 0.40 XAa = 0.12 XAs = 0.48

Lsn /B = 3

Chemical Reaction Engineering Series Reactions: Given the isothermal, constant volume, elementary batch reactions: A→2R→S with Cao = 2.5M, Cro = 0.1M, k1 = 0.25/min and k2 = 0.5L/mole-min, determine Cr after 4minutes using R-K method with a stepsize (h) = 1. Graph time versus concentration after. SOLUTION: