9.6-2) Prediction of Effect of Process Variables on Drying Rate . Using the conditions in example 9.6-3 for the constant rate drying period, do as follows: a Predict Predict the effec effectt on Rc ifif the the air velocity velocity is is only only 3.! 3.! m"s #
Predict Predict the the effect effect if the gas temperat$ temperat$re re is raised raised tom %6.%&' %6.%&' and and it remain remains s the same. same.
()*+: rom example 9.6-3 / .0!% x .0!% m # / 1!.0 mm v / 6.2 m"s d# / 6!.6&' 4 / .2 5g 41"5g d.a R+7U)R+8: a
Rc if v / 3.! m" m"s
#
Rc with / %6.6&'
U): a; rom ex. 9.6-3
ρ = 1.037
kg m
#; < / %6.%&'
3
4 / .2 5g 41"5g d.a
V H = ( 2.83 x10
G = vρ m s kg = 3.05 3600 1.037 s hr m 3
=
−3
+
4.56 x10
H )T
−3
[( 2.83x10 ) ( 4.56 x10 )( 0.010) ]( 273 -3
−3
+
G = 11386.26 kg m2 /h VH = 1.0056 m 3 /kg da
h = 0.0204G 0.8 =
ρ =
(
0.0204 11386.26
h = 35.8703
Rc =
h
λ W
W m
2
−
K
1.0056
= 1.0044
kg m
3
G = vρ s k g m = 6.1 3600 1.0044 hr m s 3
( T − T W )
35.8703 =
)
0.8
1.0 + 0.010
(
2433 1000
)
( 65.6 − 28.9) ( 3600 )
G = 22056.1447 kg/ h-m 2
h = 0.0204G 0.8 =
Rc = 1.9479 g! " 2 -#
(
0.0204 22056.1447
h = 60.8771
W m
2
−
K
)
0 .8
+ 76.7
)
Rc =
h
λ W
( T − T W )
60.8771 =
(
2433 1000
)
Rc = 4.21 g!#-" 2
( 76.7 − 28.9)( 3600 )
9.3-1 Humidity from Vaor !r"##ur". $G"a%ko&i#' he air in a room is at 3%.=o' and a total Press$re of 22.3 >pa a#s. containing water vapor with a partial press$re p / 3.!9 >Pa. 'alc$late: a; 4$midity #; at$ration h$midity and percentage 4$midity c; Percentage Relative 4$midity
@4and#oo5: a#le 1-=; < 3%.= o' / 32.= > Po / 6!9.6%660 Pa Po / 6.!9% >Pa
a; 4$midity, 4
[
MW water P A Humidity , H = MW air P T − P0 A H =
18
[
3.59
29 101.3− 6.65097
#; at$ration 4$midity, 4s
[
]
0
=.0235
MW water P A Hs= MW air PT − P0 A H =
c;
18
[
6.65097
29 101.3− 6.65097
]
] kg H 2 O Kg dry air
]
=.0426
kg H 2 O Kg dry air
Percent R4
%RH = %RH =
H ( 100 ) Hs .0235 .0426
( 100 ) =55.1643
9.3-6 (dia)ati* +aturatio% of (ir ir enters an adia#atic sat$rator having a temperat$re of %6.% o' and a dew-point temperat$re of 0.6 o'. )t leaves the sat$rator 9 ? sat$rated. Ahat are the final val$es of
)t is proposed to install a #atch drier large eno$gh to handle 3! l# dry solids containing 11l# water. rom the following data, calc$late the total drying time reC$ired.
'ritical free moist$re content / .!
lb H 2 O lb dry solid
+C$ili#ri$m moist$re content / .0
lb H 2 O lb dry solid
Doist$re content of prod$ct / .=
lb H 2 O lb dry solid
he c$rve for the falling rate period is a straight line. he rate of drying at a constant rate lb period is .6 min . (iven: eed, 3! l# dry solids lb H 2 O lb dry solid
8R)+R
E 1/ .=
11 l# water Rc/ .6 ReCGd: t / B olGn: ss$me: / 2ft1 ree Doist$re: EH / .0 X 1 =
320 350
−¿ .0 / .!=66
E1 / .= I .0 / .0 Ec / .! I .0 / .06
t /
Ms Xc [ ( X 1− Xc ) + Xc ln ] ARc X 2 350
t /
0.6 ( 1 )
[ 0.5866−0.46 )+ 0.46 ln 0.46 ¿
t / %19.12%2 min
0.04
lb min F Ec/ .!
lb H 2 O lb dry solid
poro$s solid is dried in a #atch dryer $nder constant drying conditions. even ho$rs are reC$ired to red$ce the moist$re content from 3!? to 2?. he critical moist$re content was fo$nd to #e 1? and the eC$ili#ri$m moist$re is 0?. ll the moist$re contents are on the dry #asis. ss$ming that the rate of drying d$ring the falling rate period is proportional to the free-moist$re content, how longs sho$ld it ta5e to dry a sample of the same solid from 3!? to !? $nder the same drying conditionsB
()*+: irst 'ondition t
/
E2 /
% hr s
Ec / E
H
t
.3! - .0
E 1 / .2
econd 'ondition
- .0
.1 - .0
/
B
/ .32
E2 /
.3! - .0
/ .6
E1 /
.! - .0
/ .26
Ec / .1 H E / .0
/ .0
R+7U)R+8: t for the 1nd condition U):
- .0
/ .32 / .2 / .26
t T =
ms Xc [( x 1− xc )+ xcln ] ARc X 2
7 Hrs=
ms lb H 2 O 0.16 [( 0.31−0.16 )+ 0.16 ln ( )] Arc 0.06 lb dry solution m R c
/
11.=63
t T , 2 nd =22.8063 [( 0.31 −0.16 )+ 0.16 ln (
0.16 0.01
)]
t T , 2 nd =13.5381 rs
wet solid is dried form 36? to =? in ! ho$rs $nder constant drying conditions. 'ritical moist$re is 20? and the eC$ili#ri$m moist$re is 0?. ll moist$re contents are on wet #asis. @a; 4ow m$ch longer @in ho$rs; wo$ld it ta5e, $nder the same drying conditions, to dry from =? to !? moist$reB @#; he solid is a 1-in thic5 sla#, 2 ft 1 and dried from #oth sides. )t has a density of21 l# dry solid"ft 3 wet solid. Ahat is the drying rate at the instant the moist$re content is =? ()*+: irst 'ondition !
2 cfm of air are to #e cooled fr0om 9L to %1L, #y the $se of a horiMontal spray type h$midifier, employing a co$nterflow of air and water. he air has an initial h$midity of .22 l# water vapor per l# of dry air. he $nevaporated water collects inside the apparat$s to #e recirc$lated to the spray noMMles, and ma5e$p water at %L is fed to the p$mp. 'alc$late the following #ased on the data given #elow:
a; cross section of spray cham#er in ft1 #; l#s of water sprayed per ho$r c;l#s of ma5e $p water reC$ired per ho$r d;length of spray cham#er in ft d; h$midity of air leaving the cham#er as l# water per l# of dry air
8ata: ss$me the spray cham#er operates adia#atically with normal #arometric press$re. Ahen spraying 21 l# water per ho$r per ft1 of cross section and employing an air rate of 10 l# of dry air per ho$r per ft1 of cross section, the overall coefficient of heat transfer is 9 NU" hr L t3 of spray cham#er.
()*+:
(x / 21 l#"hr.ft1 (y/ 10 l# d.a" hr.ft1 U / 9 Nt$"hr.L.ft3 R+7U)R+8: a; #; a c; l#s of ma5e$p water d; Ot
ir entering an adia#atic cooling cham#er has a temperat$re of 31.1
℃
and a
percentage relative h$midity of 6!?. )t is cooled #y a cold water spray and sat$rated with water in the cham#er. fter leaving, it is heated to 13.9
℃
. he final air has a ?
relative h$midity of 0?. @a; what is the initial h$midity of the airB @#; what is the final h$midity after heatingB @c; what is the temperat$re #efore heatingB (iven:
