Zenith^® Pumps Volumetric Efficiency of Gear Pumps

[Volumetric Efficiency] [Pump Selection Criteria]

A gear pump can be modeled as a zero clearance pump and a device which contains a narrow gap, as shown on figure 1 above. The narrow gap represents the gear clearances inside the pump. The flow being moved by the pump is:

The fluid flowing through the narrow gap is directly proportional to the pressure differential across the gap and inversely proportional to the viscosity of the fluid.

The assumption that a narrow gap represents the internal clearances of a gear pump is a rough approximation. The geometry of the actual clearances is much more complicated and, in addition, some of the surfaces are in motion, which introduces some dynamic effects that are neglected here. However, for the purpose of this analysis, the narrow gap assumption is accurate enough as we will demonstrate later on.

Volumetric Efficiency

The volumetric efficiency of a gear pump is the ratio between the actual flow rate f₃ and the theoretical flow rate f_1.

The factor k/C we will call the pump efficiency constant k_e and is a function of the pump geometry, its clearances, and its size or capacity. In other words, each pump has its own k_e value. Now we can express the efficiency of a gear pump as:

The factor DP / (N*µ) is a function only of the operating conditions of the pump, which means that the volumetric efficiency of a gear pump depends on how the pump is used.

The above expression for pump efficiency can be represented graphically in Cartesian coordinates or in Logarithmic - Cartesian coordinates.

Figure 2 - Efficiency curves of a gear pump with an efficiency constant k_e = 0.25.

The efficiency expression as presented in equation #2.0 is an approximation, which assumes that there is a linear relationship between the pump efficiency and the factor DP / (N*µ). This approximation tends to be more accurate if we consider a small range of DP / (N*µ). In other words, the pump efficiency curve is closer to a straight line if we only look at a small portion of the curve.

In the case of a high precision gear pump with small k_e value we are only interested in the small portion of the curve where the pump operates as a metering device. If we want the pump to operate at high efficiency rates, say 90% or higher, the range of operation is:

since substituting (10*k_e)^-1 for DP / N*µ) in eq. 2.0 results in h= .9. For this small range the narrow gap approximation is sufficiently accurate, which has been demonstrated with experimental data.

The pump efficiency constant can be determined empirically from laboratory test data running the pump at various values of DP / (N*µ) and using two or three fluids of different viscosities.

From the pump efficiency expression, h = 1 - k_e * DP / (N*µ) (eq. 2.0), we can conclude the following:

• The higher the pressure differential across the pump, the lower the volumetric efficiency.
• Pumps operate at higher efficiency with more viscous fluids.
• At higher speed of operation, the pump is more efficient.
• Pumps with small value of pump efficiency constant are more efficient.
• The flow rate of a pump running at small values of DP / (N*µ) is less sensitive to changes in the systems. For instance, in the case of a pump running at low efficiency, say 65%, a 15% increase in DP will result in a 8% drop in flow rate. If the same pump is running at 96% efficiency, the same DP increase of 15% will result in only 1% change in flow rate.
• Changes in viscosity due to temperature fluctuations will also cause large variations in flow rate if the pump is running at low efficiency or a large value of DP / (N*µ).

Pump Selection Criteria

If the pump efficiency constant k_e is known, the efficiency equation can be helpful in selecting the appropriate pump for the application. For a given application the smallest pump should be selected to keep the pump speed high, yielding a higher efficiency. For cost reasons, the smallest pump speed is also desirable. However, the pump speed is limited by the design features of the pump (i.e., materials of construction, running clearances, bearing design, etc.) Therefore, the pump speed should be kept under the maximum allowable recommended by the manufacturer.

For metering applications the selected pump should run at high volumetric efficiency. Therefore, the pump selection criteria should be:

where h_s = specified minimum efficiency. The following are some useful values:

K_e Values for Calculating Pump Efficiency

Metering System Design Requirements

Seal Selection & Application