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Pump Characteristic curve; the head produced reduces with the discharge of the pump. Pump curves are quite useful in the pump selection, testing, operation and maintenance. Pump performance curve is a graph of differential head against the operating flow rate. They specify performance and efficiency characteristics.
If an NPSH A is say 10 bar then the pump you are using will deliver exactly 10 bar more over the entire operational curve of a pump than its listed operational curve. Example: A pump with a max. pressure head of 8 bar (80 metres) will actually run at 18 bar if the NPSH A is 10 bar. i.e.: 8 bar (pump curve) plus 10 bar NPSH A = 18 bar.
These are called the pump curves. They are determined by studies, whose methodology is standardized. These curves are specified when water is pumped with a density of 1000 kg/m3 and kinematic viscosity of 1 mm2/s. When the circulating pump is used for liquids of different density and viscosity, the pump curves have to be recalculated.
The affinity laws (also known as the "Fan Laws" or "Pump Laws") for pumps/fans are used in hydraulics, hydronics and/or HVAC to express the relationship between variables involved in pump or fan performance (such as head, volumetric flow rate, shaft speed) and power. They apply to pumps, fans, and hydraulic turbines. In these rotary implements ...
When the model has been estimated over all available data with none held back, the MSPE of the model over the entire population of mostly unobserved data can be estimated as follows.
A variation of the Theil–Sen estimator, the repeated median regression of Siegel (1982), determines for each sample point (x i, y i), the median m i of the slopes (y j − y i)/(x j − x i) of lines through that point, and then determines the overall estimator as the median of these medians.
In the bottom-right graph, smoothed profiles of the previous graphs are rescaled, superimposed and compared with a normal distribution (black curve). Main article: Central limit theorem The central limit theorem states that under certain (fairly common) conditions, the sum of many random variables will have an approximately normal distribution.
Statistical packages implement the ARMAX model through the use of "exogenous" (that is, independent) variables. Care must be taken when interpreting the output of those packages, because the estimated parameters usually (for example, in R [15] and gretl) refer to the regression: