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How do we calculate unbalanced horizontal load, amplitude and mass movement?

Q: We have a mixing vessel (diameter 2,000 mm , height 2,200 mm, weight 4,000 kg). It is an anchor type mixer -- length 1,900 mm (tip blade 2no.,180D, diameter 11 in., 2nd step 800 mm - blade 2no.,180D, perpendicular to associate steps, diameter 9 in., 3rd step 1,600 mm - blade 2no.,180D, diameter 6 in.);140 rpm; 3no. baffle 120D spacing.

We mix sulphuric acid (sp. gr. 1.80) = 5,000 kg, LAB (sp. gr.0.85) = 2,500 kg, water =1,000 kg.

How do we calculate unbalanced horizontal load, amplitude of the vessel, and mass movement of inertia for proposed 4 lug support?

A:

I will provide my answer based on my best understanding of the questions and conditions:
 
Tank Diameter: 2,000 mm
Tank Straight-Side Height:  2,200 mm
Weight: (tank? or contents?) 4,000 kg (makes no difference on the answer)
 
Sulfuric Acid:
    100 cp (sufficient estimate)
    1.8 sp. gr. (specified - max. value for design)
 
Bottom Impeller:  Anchor Type (contoured to bottom of tank) Diameter: 1,900 mm, 2 blades, 11 inches wide (?)

Middle Impeller: Diameter: 800 mm, 2 blades, 9 inches wide (mounted at 90 degrees to bottom impeller - makes no difference in the answer)

Top Impeller: Diameter 1600 mm, 2 blades, 6 inches wide (mounted at 90 degrees to middle impeller - makes no difference in the answer)
 
Rotational Speed, not specified, but critically important:  Estimated speed 0.25 revolutions per second -- based on reasonable mixing intensity
 
Motor Power: Not specified but estimated at 7.5 KW.    Motor power should be the design basis for mixer load on impellers.
 
Worst case design scenario assumes that impellers will occasionally operate at the liquid level as tank is either filled or emptied, necessitating a high horizontal load on the upper impeller.  Same higher load expected on lower impellers, but only when liquid level is below upper impeller.
 
Shaft design, support forces, and moment of inertia all depend on impeller locations (distance from support), none of which were specified in question:
 
Estimated horizontal forces:
Upper Impeller: 924 Newtons
Middle Impeller: 39 Newtons
Bottom Impeller: 477 Newtons
 
For a more detailed explanation, I suggest reading Chapter 21, Mechanical Design of Mixing Equipment, in "Handbook of Industrial Mixing," (John Wiley, 2004).
 
Complete answer and explanation would require more complete information about impeller sizes, blade widths, location with respect to mounting, rotational speed, and motor power.  Probably would necessitate drawings or much more information and a design study on fee basis.

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