CHEMICAL ENGINEERING

14 CHEMICAL ENGINEERING VOLUME 1 SOLUTIONS

In equation (i): u 0 Dd^2 g/ 18 
s


 2 ð 10 ^7 /dDd^2 ð 9. 81 / 18 ð 0. 001  1600  1000 

∴ d^3 D 6. 12 ð 10 ^13

and: dD 8. 5 ð 10 ^5 mor 85μm

PROBLEM 1.

A sphere, initially at a constant temperature, is immersed in a liquid whose temperature
is maintained constant. The timettaken for the temperature of the centre of the sphere
to reach a given temperature"cis a function of the following variables:

Diameter of sphere,d

Thermal conductivity of sphere,k

Density of sphere,

Specific heat capacity of sphere,Cp

Temperature of fluid in which it is immersed,"s.

Obtain relevant dimensionless groups for this problem.

Solution

In this case,tDfd,k,
,Cp,"c,"s. The dimensions of each variable are:tDT,dD
L,kDML/Tq,CpDL^2 /T^2 q,"cDq,"sDq. There are 7 variables and hence with 4
fundamental dimensions, there will be 7  4 D3 dimensionless groups. Takingd,
,Cp
and"cas the recurring set, then:

dL, LDd,

M/L^3 , MD L^3 D

d^3

"cq, qD"c

CpL^2 /T^2 q CpDd^2 /T^2 "candT^2 Dd^2 /Cp"cor:TDd/Cp^0.^5 "^0 c.^5

Thus: dimensionless group 1:t/TDtCp^0.^5 "c^0.^5 /d

dimensionless group 2:kTq/MLDkd/Cp^0.^5 "^0 c.^5 "c/

d^3 dDk"c^0.^5 /Cp^0.^5 

d^3

dimensionless group 3:"s/qD"s/"c

PROBLEM 1.

Upon what variables would the rate of filtration of a suspension of fine solid particles be
expected to depend? Consider the flow through unit area of filter medium and express the
variables in the form of dimensionless groups.
It is found that the filtration rate is doubled if the pressure difference is doubled. What
would be the effect of raising the temperature of filtration from 293 to 313 K?