Chemical Engineering Answers

10)Using Residue theorem evaluate ∮c Z cosh πz/Z^(4)+5Z^(2)+4, where C is |z| = 3.

9)Find Laurent series expansion of the function 1/ z²+z-6 in the regions

1<|z-1 <4 and |z-1|> 4.

8)Show that u(x, y) = 4y + 3x²y-y³ is harmonic and find its conjugate harmonic function v(x, y).

7) Show that the function f(z)={(z̅ )^2,Z≠0. ; 0,Z=0 satisfies Cauchy-Rieman equations at z=0.Does f'(0) exists?

3) Find Laplace transform of the function f(t)={t, 0≤t<1 ; 2-t,1≤t≤2 and f(t+2)=f(t)

2. A mixture containing benzene and toluene with 40% benzene and 60% toluene is to be separated in a fractionating column to give a product containing 96% benzene, bottom product containing 95% toluene. Feed is mixture of two third vapor and one third liquid. Find out the number of theoretical stages required if the reflux ratio of 15 times the minimum is used. Relative volatility is 2.5(McCabe Thiele Method), explain step by step with lengthy process?

A step change of magnitude 10 is introduced into the transfer function

Y(S)/X(S)= 4/(2S²+0.3S+0.5),

find the following

a. Percent overshoot.

b. Rise time

c.Maximum value of y(t)

d. Ultimate value of Y(t)

e. Period of oscillations.

Explain briefly with step by step process.

1. A mixture containing 10% ethanol (E) and 90% H₂O (W) by weight is fed into a distillation column at the rate of 106.26 kg/h. The distillate (top product) contains 94.01 % ethanol and the distillate is produced at a rate of one tenth of that of the feed. 
2. _{Draw and label a flow chart of the process before solving the problem. Perform material (total) and ethanol balances to calculate the mass fraction of ethanol in the bottom product to at least four decimal places.} 

Liquid reactant decomposes as per the following reaction scheme: A→R, A→S with rates rR= k1CA^2₁ , rs=k₂CA The rate constants are k=0.4 m³/mo min and k=2 min³. An aquecus feed of containing A with CAo =40 mol/m³ enters a reactor, decomposes, and a mixture of A, R and S leaves the reactor. Find the operating condition (XA, τ and CR) which maximizes CR, in a mixed flow reacter.