Discharge coefficients, liquid flow

Maximum operating pressure, 33 Diaphragm metering pump, 214 DIERS, final reports, 523 Discharge coefficients, liquid flow, Q, chart, 118... 

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... 

Figure 2-18. Flow coefficient C for square edged orifices. By permission, Crane Co. [3], Technical Paper 410 Engineering Div. (1976) and Fluid Meters, Their Theory and Application Part 1, 6th Ed., 1971, American Society of Mechanical Engineers and, Tuve, G. L. and Sprenkle, R. E., Orifice Discharge Coefficients for Viscous Liquids, Instruments Nov. 1933, p. 201.

Figure 2-39. Discharge coefficients for liquid flow. By permission, Cameron Hydraulic Data, Ingersoll-Rand Co., Washington, N.J., 1979.

At = total tower cross-sections, area, ft-Cq = vapor discharge coefficient for dry tray g = acceleration of gratdty, 32.2 ft/sec hj, = head loss due to vapor flow through perforations, in. liquid... 

A venturi meter with a 50 mm throat is used to measure a flow of slightly salty water in a pipe of inside diameter 100 mm. The meter is checked by adding 20 cm3/s of normal sodium chloride solution above the meter and analysing a sample of water downstream from the meter. Before addition of the salt, 1000 cm- of water requires 10 cm3 of 0.1 M silver nitrate solution in a titration. 1000 cm3 of the downstream sample required 23.5 cm3 of 0.1 M silver nitrate. If a mercury-under-water manometer connected to the meter gives a reading of 20S mm, what is the discharge coefficient of the meter Assume that the density of the liquid is not appreciably affected by the salt. 

This equation defines the flow coefficient, Cv. Here, SG is the fluid specific gravity (relative to water), pw is the density of water, and hv is the head loss across the valve. The last form of Eq. (10-29) applies only for units of Q in gpm and hv in ft. Although Eq. (10-29) is similar to the flow equation for flow meters, the flow coefficient Cv is not dimensionless, as are the flow meter discharge coefficient and the loss coefficient (Af), but has dimensions of [L3][L/M]1/2. The value of Cv is thus different for each valve and also varies with the valve opening (or stem travel) for a given valve. Values for the valve Cv are determined by the manufacturer from measurements on each valve type. Because they are not dimensionless, the values will depend upon the specific units used for the quantities in Eq. (10-29). More specifically, the normal engineering (inconsistent) units of Cv are gpm/ (psi)1/2. [If the fluid density were included in Eq. (10-29) instead of SG, the dimensions of Cv would be L2, which follows from the inclusion of the effective valve flow area in the definition of Cv]. The reference fluid for the density is water for liquids and air for gases. 

Cv control valve discharge coefficient for liquid flow, [L7/2/M1/2]... 

Calculate the volumetric flow rate in m3/s through a V-notch weir when the height of liquid above the weir is 0.15 m given that the notch angle 6 = 20° and the discharge coefficient Cd - 0.62. 

Suitable values of discharge coefficient for different situations are given in BS 2915[13] for single phase liquid or gas flow. CCPS1141 indicate that a gas discharge coefficient should be used for two-phase flow provided the flow chokes, otherwise a liquid discharge coefficient should be used. 

Either Qi or Q2 or both may be variable and functions of z, or one of the two may be either constant or zero. For example, if liquid is discharged through an orifice or a pipe of area A under a differential head z, Q2 = Cd (2gz)m, where Cd is a numerical discharge coefficient and z is a variable. If the liquid flows out over a weir or a spillway of length B, Q2 = CBz3/2, where C is the appropriate coefficient. (For steady flow, z would be the constant H.) In either case z is the variable height of the liquid surface above the appropriate datum. In like manner, Qi may be some function of z. 

Morris, S.D. Liquid flow through safety valves diameter ratio effects on discharge coefficients, sizing, and stability. J. Loss Prev. Process Ind. 1996, 9 (3), 217-224. 

Figure 5-1 shows the locations and names of the orifice taps. The true mass flow rate for both liquids and gases is obtained by multiplying the theoretical mass flow equation by the discharge coefficient, the gas expansion factor, and the thermal-expansion factor. This is expressed as ... 

Flow rate of bottoms product, mol/h, kg/h or Ib/h Discharge coefficient, flow through perforations of sieve plate Specific heat at constant pressure, J/g-°C or Btu/lb-°F Cp, of condensate Cpx, of liquid Cpy, of vapor Flow rate of overhead product, mol/h, kg/h or Ib/h Diameter of column, m or ft Eddy diffusivity, m /s... 

One proposed simplified theory (4) provides reasonably accurate predictions of the internal flow characteristics. In this analysis, conservation of mass as well as angular and total momentum of the liquid is assumed. To determine the exit film velocity, size of the air core, and discharge coefficient, it is also necessary to assume that a maximum flow through the orifice is attained. 

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