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Eductor Pump Design Equations

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Fluids Flow Design and Engineering

Eductor Pump Design Equations

General Purpose Eductor have a capacity (flow rate) for a general purpose eductor used for pumping and blending. This type of eductor, has a broad performance span rather than a high peak efficiency point. Standard construction materials for this type of eductor are cast iron, bronze, stainless steel, and PVC. Typical uses include cesspool pumping, deep-well pumping, bilge pumping aboard ship, and condensate removal.

Beside the obvious advantages of being self-priming, having no moving parts, and requiring no lubrication, eductors can be made from any machinable material in addition to special materials, such as, tubing, heat-resistant glass, and fiberglass. The applications throughout industry are too numerous to mention, but some of the more common will be discussed here. The type of eductor is determined by the service intended.

The elements of a fluid eductor design are shown in Figure 1.

Eq. 1,
Operating head
h₁ = P₁ - P_s / γ₁

Eq. 2
Discharge head
h_d = P₂ - P_s / γ₂

The head ratio R_H is defined as the ratio of the operating head to the discharge head:

Eq. 3
Head Ratio
R_H = [ ( P₁ - P_s ) / γ₁ ] / [ ( P₂ - P_s ) / γ₂ ] = [ ( P₁ - P_s ) γ₂ ] / [ ( P₂ - P_s ) γ₁ ]

Because ratios are involved, it is convenient to replace specific weight with specific gravity:

Eq. 4
Head Ratio
R_H = [ ( P₁ - P_s ) ( sp. gr.₂ ) ] / [ ( P₂ - P_s ) ( sp. gr.₁ ) ]

When the suction and motive fluids are the same, no gravity correction is required and Eq. 4 becomes

Eq. 5
Head Ratio
R_H = ( H₁ - H_s ) / ( H₂ - H_s )

Eq. 6
Operating head
h₁ = H₁ - H_s

Eq. 7
Discharge head
h_d = H₂ - H_s

Where

h₁ = operating head, ft, (m)
h_d = discharge head, ft, (m)
P₁ = static pressure upstream, lb/ft² (N/m²)
P₂ = static pressure at discharge, lb/ft² (N/m²)
P_s = static pressure at suction (nozzle tip), lb/ft² (N/m²)
V  velocity, ft/s (m/s)
γ₁ = specific weight (force) of motive fluid, lb/ft³ (N/m³)
γ₂ = specific weight (force) of mixed fluids, lb/ft³ (N/m³)

*A short tube has a length less than approximately 3 diameters.

Figure 1 - Eductor elements and terminology

Source:

Pump Handbook, Third Edition
Igor J. Karassik
Joseph P. Messina
Paul Cooper
Charles C. Heald

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