It is desired to build a centrifugal pump geometrically...

It is desired to build a centrifugal pump geometrically similar to that of Prob. P11.28 to deliver 6500 gal/min of gasoline at $20^{\circ} \mathrm{C}$ at $1060 \mathrm{r} / \mathrm{min}$. Estimate the resulting $(a)$ impeller diameter, $(b)$ head $(c)$ brake horsepower, and $(d)$ maximum efficiency.

Key Concepts

Brake Horsepower Calculation

Brake horsepower represents the actual power output required by the pump’s driver to overcome hydraulic and mechanical losses in the system. Calculating brake horsepower involves determining the hydraulic power based on flow and head, and then adjusting for the efficiency of the pump, providing an estimate of the energy that must be supplied to achieve the desired performance.

Pump Performance Characteristics

Pump performance characteristics include parameters such as flow rate, head, and efficiency, which describe how effectively a pump moves fluid and converts mechanical energy into hydraulic energy. Understanding these parameters is essential for designing and scaling pumps to meet specific operational requirements while maintaining energy efficiency.

Geometric Similarity

Geometric similarity in pump design means that two pumps have identical shapes and proportions, with dimensions differing by a constant scale factor. This concept ensures that the flow patterns and stress distributions are similar in both pumps, allowing engineers to predict the performance of a new pump based on an existing model using scaling relationships.

Pump Affinity Laws

The pump affinity laws are scaling relationships that connect the performance parameters of pumps—namely, flow rate, head, and power—to the pump’s rotational speed and impeller diameter. They allow for the estimation of how changes in size or speed affect performance, with flow rate scaling with the cube of the diameter and speed, head scaling with the square, and power with the fifth power, under geometrically similar conditions.

Dimensional Analysis

Dimensional analysis is a mathematical tool used to derive relationships between physical quantities by considering their units. In the context of pump design, it is used along with geometric similarity to establish the proportionality laws that predict how alterations in size, speed, or fluid properties will impact pump performance.

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