## Basic Pumping Calculations

Calculations, calculations, calculations, and more calculations! Indeed, we cannot get away from them—not in water/wastewater treatment, collection and distribution operations, licensure certification examinations, nor in real life. Basic calculations are a fact of life that the water/wastewater maintenance operator must accept and should learn well enough to use as required to operate a water/wastewater facility correctly. The following sections address the basic calculations used frequently in water hydraulics and pumping applications. The basic calculations that water and wastewater maintenance operators may be required to know for operational and certification purposes are also discussed. In addition, calculations for pump specific speed, suction specific speed, and affinity, among other advanced calculations, are also covered in the following sections, although at a higher technical level.

### 10.2.1 Velocity of a Fluid through a Pipeline

The speed or velocity of a fluid flowing through a channel or pipeline is related to the cross-sectional area of the pipeline and the quantity of water moving through the line; for example, if the diameter of a pipeline is reduced, then the velocity of the water in the line must increase to allow the same amount of water to pass through the line.

Cross-Sectional Area (ft2) A

Problem: If the flow through a 2-ft-diameter pipe is 9 MGD, what is the velocity?

Solution:

Problem: If the same 9-MGD flow used in Example 10.1 is transferred to a pipe with a 1-ft diameter, what would the velocity be?

Solution:

9 MGD x 1.55 cfs/MGD _ 14 cfs 0.785 x 1 ft x 1 ft _ 0.785 ft2

Velocity =-^ '-> a—v^-= ~ ^r- - 2 = 17 8 fps (rounded)

Based on these sample problems, you can see that if the cross-sectional area is decreased the velocity of the flow must be increased. Mathematically, we can say that the velocity and cross-sectional area are inversely proportional when the amount of flow (@) is constant.

Area1 x Velocity1 = Area2 x Velocity2 (10.2)

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