Calculation and Design of Critical Speed and Power Agitator

Design of Agitator 8 Batch Volume 6 Vessel Diameter 6 Agitator diameter Agitation rpm Overhang of agitator between shaft bearing & agitator No of Agitator Properties of reactor contents Density Viscosity

V T D N

= = = =

4 1.5 0.6 100

l

=

3

n

=

2

ℓ µ

= =

1200 100

Np P

= = = = = =

4.8 5.637 0.564 1.240 7.44

= = = =

SS304

rpm m

kg/m3 cp

Agitator Data 7 Agitator Type

Calculation Power Requirement Power Number Power Required Gland Loss (10%) Transmission loss (20%) Total requirement Rounding to

P P

7.00

hp hp hp hp

Agitator shaft diameter Select shaft MOC

Permissible shear stress, fs Elastic limit , f Modulus of Elasticity, E Output Torque, Tc Max. torque, Tm Polar modulus of section of c/s , Zp (d)3 d Force acting on radius from the axis of agitator shaft, Fm Bending moment, M Equivalent bending moment, Me Elastic limit, f

40 260 210000

N/mm2 N/mm2 N/mm2

= = = = =

498917.2 N-mm

748375.8 N-mm 18709.39 mm3 95334.5 mm3 45.68 mm

= = = =

3326 9978344 9992356 1068

N N-mm N-mm N/mm2

Elastic limit is greater than permissible limit,Change agitator diameter, d

d Elastic limit, f

= =

95 119

mm N/mm2

Elastic limit is within permissible limit

Deflection of Shaft (D): = =

I

D

3996171 mm4 36 mm

Critical Speed (Nc): Nc

=

158

rpm

Actual speed as % of critical speed

=

63.1

%

Design is Satisfactory Checked with critical speed. Note: Actual speed of agitator should be 40 to 65 % of the critical speed and should not be

70 to 130 % of the critical speed.