Design criteria for a pumping station
The classic scheme of a pumping station foresees a suction pipe, the pump and a delivery pipe. The geodetic head is defined as the difference in Hg level existing between the two tanks connected by the system, while the total head Ht is the difference between the total loads in the two sections immediately upstream and downstream of the pump. In the more general situation it results:
(1)
having indicated with Ya and Ym the continuous pressure losses that occur, respectively, in the suction and delivery ducts, with Λi the localized inlet loss and with Λs that of outlet. In the case of long pipelines, the kinetic heights are neglected compared to the piezometric ones (coincidence of the line of total loads with the piezometric) and therefore the total head Ht coincides with the manometric head which is equal to the difference between the piezometric heights in the two sections placed immediately upstream and downstream of the pump. In the case of long pipelines, since localized pressure drops are neglected, (1) becomes:
(2)
To raise an assigned flow rate Q with a total head Ht from the lower tank to the upper one, it is necessary to use a pump with power P equal to:
(3)
where the power is expressed in CV, the range in m3 / s, the total head in m, γ is the specific weight of the liquid to be lifted expressed in kg / m3 and η is the efficiency of the pump or electric pump motor unit which represents the efficiency of the operating machine in converting the power generated by the motor (electric or thermal) coupled to the pump into hydraulic power. In the ideal case η = 1 and this means that all the engine power would be converted into hydraulic power.
If we want to express the power P in kW, without prejudice to the units of measurement of the hydraulic quantities, (3) is written:
(4)
Project of a lifting system
The resolution of the design problem of a lifting system for which the geodetic prevalence Hg, the overall length L of the pipeline (suction and delivery) to be made with constant diameter D are assigned and the material with which to make the piping has been chosen (steel , PVC, polyethylene, etc.) consists in the calculation of the diameter D to be assigned to the pipes and in the determination of the pump power P. For each preselected value of the diameter D through the equation of motion
(5)
it is possible to calculate the total head Ht and then by means of (4), known γ, Q, η and Ht, to evaluate the power P. In other words, for each value of the hypothesized diameter, (4) and (5) lead to a solution to the problem. It should be noted, however, that as the diameter of the pipe increases, the overall head loss in the long pipe L decreases and therefore, by decreasing the total head, the power P of the pump to be used also decreases. A decrease in power involves a reduction in the energy costs that must be incurred to operate the plant and therefore a decrease in the annual operating cost of the plant.
As the diameter increases, reported to the year, ie expressed as the annual depreciation rate of the plant, correspond to higher plant costs Ci which substantially identify with the cost of the pipes. In conclusion, as the diameter D of the pipe adopted increases, the annual operating cost Ce decreases and the plant cost Ci increases.
The following graph shows the two functions Ce (D) and Ci (D) and the total cost function C, obtained by adding the sum of the plant and operating costs. The total cost function admits a minimum. There is therefore a solution of maximum economic benefit, minimum value of the total cost (Cmin), which corresponds to a project diameter Dp.
