Discharge Measurements

29.9 Discharge Measurements

Discharge measurements are made for monitoring and control purposes. Measurement methods may be divided into those for pipe and those for open-channel flows. The following summarizes some results for both types.

Pipe Flow Measurements

Traditional methods for measurements of discharge, Q, in a pipe of diameter, D, and cross-sectional area,

A, have depended on the production of a pressure difference, Dp, across a device constricting the flow. Foremost among such devices are various types of orifice and Venturi meters, the basic theory of which has been outlined in Appendixes 5 and 6.

In general, Q is related to the difference in piezometric head across the device, Dh, by

2 g () D h (29.30)

where A o is cross-sectional area of the contraction, and b = d/D, d being the diameter of the contracted section. The discharge coefficient, C d , may vary according to the device, the exact location of the pressure taps where the measurements are made, b and Re. The head loss across the device, h m , is given as fraction of measured differential pressure head.

The common thin-plate orifice meter is square-edged and concentric with the pipe ( Fig. 29.18a ). It is used for clean fluids and is inexpensive, but is associated with relatively high head loss. Miller (1989) gives a correlation for C d for an orifice with corner taps:

C . 0 5959 0 0312 . 21 . . 0 184 8 . 91 71 d b = + b - b + 0 75

Re .

FIGURE 29.18 Pipe flow-measuring devices. (a) Thin-plate orifice with corner pressure taps. (b) Venturi tube.

and a correlation for h m as

h m =-

1 0 24 . b - . 0 52 b 2 - . 0 16 b 3 (29.32)

D h These correlations are valid for 0.2 < b < 0.75 and 10 4 < Re < 10 7 .

In comparison to orifice meters, the Venturi meter ( Fig. 29.18b ) incurs low head losses, is suitable for flows with suspended solids, and exhibits less variation in performance characteristics. Disadvantages include higher initial cost and the length and weight of the device. C D for a Venturi meter ranges from 0.975 to 0.995 (for Re > 5 ¥ 10 4 ), while h m / Dh varies with the exit cone angle as (Miller, 1989)

Various other flow meters are in use, and only a few are noted here. Elbow meters are based on the pressure differential between the inner and the outer radius of the elbow. Attractive because of their low cost, they tend to be less accurate than orifice or Venturi meters, because of a relatively small pressure differential. Rotameters or variable-area meters are based on the balance between the upward fluid drag on a float located in an upwardly diverging tube and the weight of the float. By the choice of float and tube divergence, the equilibrium position of the float can be made linearly proportional to the flow rate. More recently developed non-mechanical devices include the electromagnetic flow meter and the ultra- sonic flow meter. In the former, a voltage is induced between two electrodes that are located in the pipe walls but in contact with the fluid. The fluid must be conductive, but can be multiphase. The output is linearly proportional to Q, independent of Re, and insensitive to velocity profile variations. Ultrasonic flow meters are based on the transmission and reception of acoustic signals, which can be related to the flow velocity. An attractive feature of some ultrasonic meters is that they can be clamped on to a pipe, rather than being installed in place as is the case of most other devices.