Calculation of pump axial force (closed impeller)

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1. Calculation of the axial force F on the impeller: Due to the rotation of the impeller, the liquid inside the pump also rotates along with it. However, the speed at which the liquid rotates is not synchronized with the speed of the impeller itself. The pressures on the front and rear cover plates can be approximated as following a parabolic distribution. If the effects of leakage at the seals are ignored, for a single-stage impeller, it can be assumed that the pressures on the front cover plates a, b, e, d are equal in magnitude but opposite in direction to those on the rear cover plates e, f, g, h. The remaining axial force is then denoted as F. In the calculation of this formula, the radial flow of the liquid as well as the uneven pressure distribution caused by misalignment between the outlet of the impeller and the inlet of the guide vanes are ignored. Nevertheless, in practical applications, this formula provides sufficient accuracy.

2. Calculation of the reaction force: Liquid usually flows axially into the impeller and exits radially or obliquely. After being affected by the forces exerted by the impeller, both the speed and direction of the liquid change. Conversely, the liquid exerts a reaction force on the impeller; this force has the same magnitude but opposite direction to that exerted by the impeller, and it is known as the reaction force. This force acts in the direction behind the impeller. The reaction force can be determined using the law of momentum. The formula for its calculation is as follows:

3. Total axial force: The formula for calculating the total axial force in a single-stage pump is as follows: F = F1 – F2. For multi-stage pumps, the formula is: F = ∑(F1 – F2)i, where i represents the number of stages in the multi-stage pump.

4. Empirical formula for total axial force: For a rough estimation of the axial force on centrifugal impellers, the following formula can be used: F = KHirπ (R2m – r2h)i, where Hi is the head produced by a single-stage impeller, in meters； The K-experiment coefficients are shown in Table 2–16. Table 2–16: Experiment coefficients K; Ns: 30–100, 120–220, 240–280. K values: 0.6, 0.7, 0.8