[How To] Design an agitator

Hii all......!!

Back with another post regarding detailed design of agitator, this is under making since last 3 months.

This post defines and elaborates the parameters like Tip speed, Reynolds number, Power number, Torque, Shaft dia, Bending moment, Stress, Modulus of elasticity, Moment of inertia, Deflection, Critical Speed.

Just before that, i'll define these terms to make them familiar.

What does tip speed mean ?

I've heard a common answer from many in mathematical term i.e., 𝝅dN/60.  It's correct but in general words, Tip speed can be defined as tangential speed of the agitator's blade tip.






What does Reynolds number mean and what does it indicate ?

That's a dimensionless number which represents the mixing / flow around the rotating agitator. It indicates the intensity of mixing such as laminar and turbulent.






What does Power number mean and what does it indicate ?

This is also a dimensionless number used for estimating power consumed by an impeller during mixing. The power number varies based on Reynolds number.

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What is torque ?

Torque will be always an underrated term in mixing by process engineers. Torque can be defined as a rotational force that will make the reaction mixture move/flow along the respective pattern that the agitators provide.






What is bending moment ?

Bending moment is nothing but the reaction of the agitator shaft due to the resistive force induced by the reaction mixture, sometimes due to the more viscousness of the mass the agitator will tend to slightly bend / sometimes it might break i.e., the coupling might get fail.






What is Modulus of elasticity ? 

It can be the measurable resistance that can be offered by the agitator towards reaction mixture before it can deform from its original position.






What is moment of inertia ?

It is the inertia of agitator towards its agitation. Now i think you may think of "what is inertia?". Additionally i'll clear you that, inertia is a property of the agitator to remain unchanged w.r.t. its RPM.






What is Critical Speed of an agitator ?

It's the speed of the agitator at which the shaft will start to vibrate violently and at this point it will reach the natural frequency and shall fail.

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Now let's get into the topic w.r.t. calculations.

Let's try our case with a 5 KL SS reactor with Anchor agitator.

Below are the inputs required and my considerations:

Inner dia of reactor: 1.82 m,
Sweep dia / Agitator dia : 1.6 m,
Agitator Speed: 60,
Motor RPM, Mr : 1475,
Reaction mass density : 1500 Kg/m3,
Reaction mass viscosity : 1.5 Kg/m-sec
Permissible Stress of SS316, Fs : 550 kg/cm2,
Shaft overhung length, L : 2.1 m,
Modulus of elasticity, E : 1950000 Kg/cm2.




Let's begin the show,

Tip speed = 𝞹 x d x N / 60 = 3.141 x 1.6 x 60 / 60 = 5.03 m/sec,

Reynolds number = N x d^2 x ⍴ / 𝝻 = (60/60) x (1.6^2) x 1500 / 1.5 = 2560,

Power number = 0.5 [as per agitator curves]

Power = Np x ⍴ x N^3 x d^5 = 0.5 x 1500 x (60/60)^3 x (1.6^5) = 7862.84 watts = 10.54 HP,

Considering losses which might occur due to transmission, gland losses, coupling losses, they would attribute to ~25%, the efficiency would reduce to 75 %,

Power, P = 10.54 / 0.75 = 14.05 HP    ~15 HP,




Torque, 𝒯 = P x 75 / (2𝞹 x N) = 15 x 75 / (2 x 3.141 x (60/60)) = 179.08 Kg-m,

Maximum Torque, 𝒯m = 2.5 x 𝒯 = 2.5 x 179.08 = 447.7 Kg-m,

Zp =  𝒯m / Fs = 447.7 x 100 / 550 = 0.814 x 100 = 81.4 cm3,

Shaft dia, Ds = (16 x Zp / 𝞹)^0.33 = (16 x 81.4 / 3.141)^0.33 = 7.4569 ~7.5 cms,

Force, F = 𝒯m / (0.75 x (d/2)) = 447.7 / (0.75 x 1.6/2) = 746.17 Kg,

Bending moment, M = F x L = 746.17 x 2.1 = 1566.95 Kg-m,

Stress on agitator, S = M / (𝞹Ds^3 / 32) = 1566.95 / (3.141 x (7.5^3) / 32) = 3785.22 Kg/cm2,

Moment of inertia, I = 𝞹 Ds^4 / 64 = 3.141 x (7.5^4) / 64 = 155.29 cm4,




Deflection, D = F x L^3 / (3 x E x I) = 746.17 x 2.1^3 / (3 x 1950000 x 155.29) = 7.61 cm,

Critical Speed, Nc = 60 x 4.987 / D^0.5 = 60 x 4.987 / (7.61^0.5) = 108.47  ~108 RPM.

Gearbox ratio = Mr / (Nc - 25) = 1475 / (108 - 25) = 17.77  ~18,

That's it, we have done .........!!!!

Hope you understood well, in coming week 'll update & provide you a data-sheet.

If any queries, pl comment,

Comments are most appreciated !!

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About The Author

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Hi! I am Ajay Kumar Kalva, Currently serving as the CEO of this site, a tech geek by passion, and a chemical process engineer by profession, i'm interested in writing articles regarding technology, hacking and pharma technology.
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