Power curve

A power curve is a plot of the power function 4 or the power number Po against the Reynolds number for mixing ReM on log-log coordinates. Each geometrical configuration has its own power curve and since the plot involves dimensionless groups it is independent of tank size. Thus a power curve used to correlate power data in a 1 m3 tank system is also valid for a 1000 m3 tank system provided that both tank systems have the same geometrical configuration. 

The power curve for the standard tank configuration is linear in the laminar flow region AB with a slope of —1.0. Thus in this region for ReM 10, equation 5.20 can be written as 

For the transition flow region BCD which extends up to ReM - 10000, the parameters C and x in equation 5.20 vary continuously. 

In the fully turbulent flow region DE, the curve becomes horizontal and the power function f is independent of the Reynolds number for mixing ReM. For the region ReM 10000 

A plot of Po against ReM on log-log coordinates for the unbaffled system gives a family of curves at ReM 300. Each curve has a constant Froude number for mixing FrM. 

Often researchers use power curves, which are a derivative of the polarization curve as the power axis is an integral expression of both the current and the voltage. The power curve is usually characterized by the short-circuit current (this popular figure of merit has little engineering consequence) and maximum derived power or power density. The last is often used as a measure of success, but it is important to note that there is hardly any practical device that operates at the maximum power density as a design point 

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Fig. 7. Control of fan performance with inlet vane control. SoHd lines marked A and N show normal performance without vanes (vanes wide open). As vanes are progressively closed, static and power curves are modified as indicated by dashed lines. Intersection ( - ) of the system resistance curve with these reduced pressure curves at points B, C, D, and E shows how imparting more spin to the inlet air reduces flow. Projecting points A to E vertically downward to the corresponding power curve locates fan power points A through E7 Power savings achieved over throttling control can be estimated by projecting points B through E vertically downward to the A power curve and comparing the value with that from the proper reduced power curve. To...

Fig. 11. Solid polymer electrolyte (SPE) fuel cell (a) cell design and (b) power curve at 25°C.

Fig. 21. Gassed power curves for constantand JF where mixer speeds = and gas rates = < Q2 < Qs-...

Fig. 6. Discharge behavior of a battery where is the open circuit voltage (a) current—potential or power curve showing M activation, ohmic, and M concentration polarization regions where the double headed arrow represents polarization loss and (b) voltage—time profile.

Figure 6.64 Typical power curve for an induction generator of 400 kW at 11.5 m/s wind speed...

Figure 7-11. Power curve for the standard tank configuration. (Source Holland, F. A. and Bragg, R. Fluid Flow for Chemical Engineers, 2nd ed., Edward Arnold, 1995.)...

The forward-curved fan blade increases the tangential velocity considerably (see Figure 27.5b). As a result, the power required will increase with mass flow, although the external resistance pressure is low, and oversize drive motors are required if the system resistance can change in operation. The backward-curved fan runs faster and has a flatter power curve, since the air leaves the blade at less than the tip speed (see Figure 27.5c). 

FIGURE 11.24 Power curves. Abscissae is the sample size required to determine a difference between means shown on the ordinate. Numbers next to the curves refer to the power of finding that difference. For example, the gray lines show that a sample size of n = 3 will find a difference of 0.28 with a power of 0.7 (70% of the time) but that the sample size would need to be increased to 7 to find that same difference 90% of the time. The difference of 0.28 has previously been defined as being 95% significantly different. 

This latter value (tp) is given by power analysis software ancl can be obtained as a power curve. Figure 11.24 shows a series of power curves giving the samples sizes required to determine a range of differences. From these curves, for example, it can be seen that a sample size of 3 will be able to detect a difference of 0.28 with a power of 0.7 (70% of time) but that a sample size of 7 would be needed to increase this power to 90%. In general, power analysis software can be used to determine sample sizes for optimal experimental procedures. 

When flow is turbulent, the power number is obtained from Figure 6.6, Chapter 6, using Re from power curves. 

Viscoelastic damping The same approach can be used in designing power transmitting units such as belts. In most applications it is desirable that the belts be elastic and stiff enough to minimize heat buildup and to minimize power loss in the belts. In the case of a driver which might be called noisy in that there are a lot of erratic pulse driven forces present, such as an impulse operated drive, it is desirable to remove this noise by damping out the impulse and get a smooth power curve. 

At low values of the Reynolds number, less than about 10, a laminar or viscous zone exists and the slope of the power curve on logarithmic coordinates is — 1, which is typical of most viscous flows. This region, which is characterised by slow mixing at both macro-arid micro-levels, is where the majority of the highly viscous (Newtonian as well as non-Newtonian) liquids are processed. 

Between the laminar and turbulent zones, there exists a transition region in which the viscous arid inertial forces are of comparable magnitudes. No simple mathematical relationship exists between Np and Re in this flow region and, at a given value of Re, N p must be obtained from the appropriate power curve. 

Power curves for many different impeller geometries, baffle arrangements, and so on are to be found in the literature/10111719 2I but it must always be remembered that though the power curve is applicable to any single phase Newtonian liquid, at any impeller speed, the curve will be valid for only one system geometry. 

Figure 7.8. Power curve for pseudoplastic fluids agitated by different types of impeller...

Interpretation While good batches of the quality produced (= 99.81% purity) have a probability of being rejected (false negative) less than 5% of the time, even if no replicates are performed, false positives are a problem an effective purity of /.t = 98.5% will be taxed acceptable in 12.7% of all cases because the found Xmean is 99% or more. Incidentally, plotting 100 (1 - p) versus /x creates the so-called power-curve, see file POWER.xls and program HYPOTHESlS.exe. 

Correlation coefficient R > 0.999 for linear calibrations alternatively the curvature coefficient n of the power curve R = kc" should be in the range 0.9-1.1 (/ = response c = concentration) no criteria for nonlinear functions... 

For each wind speed value (v) from the cut-in (ci) to the cut-out (co) phase of the WTG, the product of its corresponding power output (Pv) multiplied by the time Hv (in hours) during which value v appears in a year is calculated. The sum of these products gives the annual energy production (WEY). Wind speed values are referred to the hub height of the turbine. The power output values, which compose the power curve of a WTG, are provided by the turbine manufacturer. Hv values are calculated from the annual distribution (or the histogram) of the wind speed values. 

Electrolyzers are generally current-controlled, which means that a certain DC is imposed according to the desired hydrogen production. In a wind-hydrogen system, the wind turbine power available for the operation of the electrolyzer is generally known therefore, the power input should be transformed to a current input. The voltage-current relation of an electrolyzer is not very simple because it depends on the temperature, pressure, and other construction characteristics. For a given electrolyzer, it is possible to experimentally establish the I-V curve at different temperatures and pressures, and deduce a temperature-dependent current-power curve. 

Regression can be performed using weighted or unweighted linear or smooth curve fitting (e.g., power curve or quadratic), but is not forced through zero. 

Figure 5.8 shows the power curve for the standard tank configuration geometrically illustrated in Figure 5.5. Since this is a baffled non-vortexing system, equation 5.20 applies.

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