Flow Coefficient

The basic form of the equation is normally modified so that the differential is expressed in pressure units and the flow coefficient is divided into the product of an experimentally deterrnined discharge coefficient, iC, and a series of calculated coefficients. In this form, for concentric restrictions ... 

Flow nozzles are commonly used in the measurement of steam and other high velocity fluids where erosion can occur. Nozzle flow coefficients are insensitive to small contour changes and reasonable accuracy can be maintained for long periods under difficult measurement conditions that would create unacceptable errors using an orifice installation. 

This equation is appHcable for gases at velocities under 50 m/s. Above this velocity, gas compressibiUty must be considered. The pitot flow coefficient, C, for some designs in gas service, is close to 1.0 for Hquids the flow coefficient is dependent on the velocity profile and Reynolds number at the probe tip. The coefficient drops appreciably below 1.0 at Reynolds numbers (based on the tube diameter) below 500. 

Although it has been common practice to specify the pressure loss in ordinary valves in terms of either equivalent length of straight pipe of the same size or velocity head loss, it is becoming more common to specify flow rate and pressure drop characteristics in the same terms as has been the practice for valves designed specifically for control service, namely, in terms of the valve coefficient, C. The flow coefficient of a valve is defined as the volume of Hquid at a specified density that flows through the fully opened valve with a unit pressure drop, eg, = 1 when 3.79 L/min (1 gal /min) pass through the valve... 

The valve cannot control if it is at either end of its travel. To ensure controUabiflty, a valve is generally chosen in such a way that at the maximum design flow rate the flow coefficient required is no more than 85% of the wide-open valve flow coefficient, and at the minimum anticipated flow rate requiring control, a flow coefficient of about 10% of the wide-open valve flow coefficient is required. Whenever practical, control valves are located at grade or at platforms, to assure adequate working space for servicing. 

Manufacturers of valves, especially control valves, express valve capacity in terms of a flow coefficient C,, which gives the flow rate through the valve in gal/min of water at 60°F under a pressure drop of 1 IbFin. It is related to K by... 

Amplitude of controlled variable Output amplitude limits Cross sectional area of valve Cross sectional area of tank Controller output bias Bottoms flow rate Limit on control Controlled variable Concentration of A Discharge coefficient Inlet concentration Limit on control move Specific heat of liquid Integration constant Heat capacity of reactants Valve flow coefficient Distillate flow rate Limit on output Decoupler transfer function Error... 

An inherent valve flow characteristic is defined as the relationship between flow rate and travel, under constant pressure conditions. Since the last two terms in Eq. (8-115) are zero in this case, the inherent characteristic is necessarily also the relationship between flow coefficient and travel. 

The flow coefficient is the capacity of the flow rate of the machine... 

Flow coefficients and pressure coefficients can be used to determine various off-design characteristics. Reynolds number affects the flow calculations for skin friction and velocity distribution. 

L sc the inlet and the last stage volume for the uncooled section and use the following equation to calculate the inlet flow coefficient 8. 

To obtain an efficiency for the geometry selected, the value of the flow coefficient must be calculated using Equation 5.19 for the first inlet and the last stage flow. 

Using the flow coefficients just calculated and Figure 5-26, the corresponding efficiencies may be looked up ... 

Willi the volumes just calculated, calculate the inlet flow coefficient fm each of the two stages using Equation 5.19. 

Look up the efficiencies for the two flow coefficients on Figure 5-27, fip =. 79 first stage efficiency t]p =. 79 last stage efficiency Pp =, 79 average of the two efficiencies... 

Use Equation 5.19 to evaluate the flow coefficient for the first and last impeller of each section. 

Step 12. Use Figure 5-27 and the flow coefficients to determine the efficiencies for the stages. 

The equations have been expressed as proportionals however, they can be used by simply ratioing an old to a new value. To add credibility to fan law adaptation, recall the flow coefficient, Equation 5.19, The term Qj/N is used which shows a direct proportion between volume Qj and speed N. Equation 5.12 indicates the head, Hp, to be a function of the tip speed, squared. The tip speed is, in turn, a direct function of speed making head proportional to speed. Finally, the power, Wp, is a function of head multiplied by flow, from which the deduction of power, proper tional to the speed cubed, may be made. 

For positive displacement pumps, a bypass-type control valve should be furnished to set the primary lube system pressure. The valve should be able to maintain system pressure during pump startup and pump transfers, which includes relieving the capacity of one pump, while both are running. The valve should provide stable, constant pressure during these transients. Flow turndown of 8 to 1 is not unusual. Multiple valves in parallel should be used if a single valve is not suitable. The valve should be sized to operate between 10 and 90% of the flow coefficient (Cv). Additional pressure control valves should be furnished as required to pro ide any of the intermediate pressure levels. 

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