Page 271 - Water and wastewater engineering

6-48 WATER AND WASTEWATER ENGINEERING

m. Determine the rotational speed required by the paddles using Equation 6-19 . Note that
the area of each paddle blade is the same, so the equation may be written

CA
Dp
3
P [( v at r1 ) 3 v ( at r2 ) 3 v ( at r3 ) ]
2
and substituting Equation 6-20 for the velocity term

CA
Dp
3
3
P 2 [ 0 75) n] [( ) 3 ( r 2 ) 3 ( r 3 ) ]
(
.
r 1
2
The area of a paddle blade is
.
.
.
Ap 015 m 3 18 m 0 477 m 2

From the length to width ratio select the appropriate value for C D .
L 3 18 m
.
21 2 .
.
W 015 m
Select C D of 1.5
Using P 232.04 W, solve the rearranged equation for n with the radii for the paddle
blades computed to the center of each blade.
⎛ 015 m⎞
.
r . m .
0425 m
0 5
1 ⎜ ⎝ 2 ⎟ ⎠
⎛ 015 m⎞
.
r . m . m
10
0925
2 ⎜ ⎝ 2 ⎟ ⎠
⎛ . m⎞
015
r 3 1 5 . m ⎜ ⎝ 2 ⎟ ⎠ 1.4425 m
/
⎛ ⎞ 1 3
n ⎜ 2P ⎟
⎜ ⎝ CA [ 2 ( 0 75)] [( ). 3 r 1 3 ( r ) 3 (r )] ⎟ ⎠
3
r
3
2
Dp
⎛ 223204 W ) ⎞ 1 3 /
(
.
⎜ ⎟
3
3
3
( ⎝ 1 000 kg/m 3 )(1 5 0 477 m 2 )( 104 65 0425) ( 0925) (11425)]⎠
. )[(
.
.
.
,
1. )(
.
⎛ ⎛ 464 08 ⎞ 1 3 /
.
/
⎜ ⎟ (165. 10 3 1 3 0 116. rpsor 6.96 rpmor rpm
7
m
)
)
.
,
(
.
( ⎝ 78 877 07 3 762)⎠
n. Assuming an efficiency of 0.65, the motor power required is
23204
.
Motor power 35698 or 357 W
.
.
065