[Gerard]

Show, for a non-washing plate-and frame filter press operating at a constant feed pressure with negligible Ve, that the optimum cycle occurs when the time for filtering equals the time lost in opening, dumping, cleaning, and reassembling the press.

The solution:

The First Desperate Attempt:

Tc = Tf (Filtration time) + Tw (Washing time) + Td (Dead Time)

At, Tw = 0, prove that Tf = Td

In a cycle:
dV = k’ (-ΔP) = k
 dT   (V+Ve)  (V+Ve)

but Ve = 0 (Negligible Ve)

therefore:

dV = k’ (-ΔP) = k
dT    (V)          (V)

by variable separable method:

(V)dV =k (dT) and integrating gives

Vf² = k Tf
2

Vf² = Tf
2k

Therefore:

Tc = Vf² + Td
       2k

redundant equation (No Tf exist)

Second Desperate Attempt:

Vf = (2k)^1/2 (Tc – Td)^1/2

dVf = (2k)^1/2 (Tc – Td)^1/2
dT

at  dVf = 0
      dT

0 = (2k)^1/2 (Tc – Td)^1/2

a redundant equation exist

The Third Desperate Attempt:

Since it is said that: Tf = Td

But, Tc = Tf + Tw + Td

But since Tw = 0

So, Tc = Tf + Td

It gives us: Tc = Tf + Tf (since, Tf = Td)

Therefore: Tc = 2Tf

But: Tc = Tf + Tw + Td , substituting this equation to the above gives,

Tf + 0 + Td = 2Tf, therefore

Td = 2Tf – Tf = Tf --------- Answer (Stupid and illogical)

can anyone give me the right answer for this problem???

[Gerard]

i have found the solution guys,
i use
d(NVf)=0
dTf

then since N=1/(Tc)=1/(Tf + Tw + Td) at Tw= o
n=1/(Tf + Td)

subsitute this to the above equation:

d(Vf/(Tf + Td))=0
dTf

but:
Vf²= Tf
2k

therefore the equation becomes:


d(Vf/(Vf/2k)²+ Td))=0
dTf


and everything after this is all deifferential equation....