## Formulas for Batch Centrifugal Machine Capacity and Gravity Factor with Online Calculator

The **batch centrifugal machines** have been using to** handle white and refined sugar massecuites as well as for affination of raw sugar in the sugar refineries.**

The batch machines were fully satisfying the sugar industry requirements for high sugar quality such as: low color, no lumps and low residual moisture content.

The purpose of this article is to evaluate the batch centrifugal machine capacity and its gravity factor

### Parameters to be required for calculation:

Basket Shell Internal Diameter in meters = D

Thickness of the massecuite in meters = e (Generally “e” value taken 0.14D for theoretical and 0.12D for practical)

Basket top plate angle to horizontal level in Deg.= θ (Generally this value having 5deg.)

Height of the basket in meters= H

RPM of the basket (maximum RPM in Cycle) = N

Time required for one cycle in sec = T

Density of the massecuite in gm/ml = S

### Formulas for Calculation :

Volume of the massecuite per cycle in M^{3 (M3/cycle) }= V = π e[ H(D-e) + e tanθ ((3D-4e)/6)]

No. of cycles per hour (cycle/hr) =C =3600/T

**Capacity of the machine (Theoretically) (Q)**

**Q = C x V in M ^{3}/hr (M^{3}/cycle x Cycle/hr)**

** =Q x S in tons/hr**

But in practically calculating the capacity of machine takes the following considerations.

1. Take 1 to 2 empty cycles during in an hour (Depends on massecuite condition) so consider one empty full cycle in total cycles per hour.

2. While charging the massecuite is always purged, spelling out some molasses such that creating space for further massecuite. This is called purging capacity. It is 10% more than theoretical capacity.

**Capacity of the machine (Practically) =Q**

**[(C-1) x V] x 1.1 in M ^{3}/hr**

**Q x S in tons/hr**

Empty Basket Shell Radius in mtrs = R = D/2

Basket Shell Radius with massecuite in mtrs = r = R-e

Mean Equivalent Radius in mtrs = Rm = 2/3 [(R^{3} – r^{3}) / (R^{2} – r^{2})]

**Gravity factor = G = Rm x 1119 x (N / 1000) ^{2}**

**Gravity factor (General formula) = G = **D x N^{2 }/ 1800

##### Explanation for gravity factor formula

Gravity Factor = Centrifugal force / Gravitational force

= m x Rm x w^{2 }/ m x g.

Where Rm is M.E.R. and

w = angular velocity = 2 π N /60 g = 9.8 m/sec^{2}

Gravity Factor =[ Rm . X 1 X (2πN / 60 )^{2 }] / 9.8

= Rm x 1119 x (N / 1000)^{2}

#### Online Calculator to find Batch Centrifugal Machine Capacity and Gravity Factor

### Please click here

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