WELL AND TOTAL DISCHARGE MEASUREMENTS
F-l. General. The simplest method for determining the flow from a pump is to measure the volume of the discharge during a known period of time by collecting the water in a container of known size. However, this method is practical only for pumps of small capacity; other techniques must be used to measure larger flows.
F-2. Pipe-flow measurements.
a. Venturi meter. The flow from a dewatering system can be accurately measured by means of a venturi meter installed in the discharge line. In order to obtain accurate measurements, the meter should be located about 10 pipe diameters from any elbow or fitting, and the pipe must be flowing full of water. The flow through a venturi meter can be computed from
V2g(h, – h2)
7.48 gal/ft3 x 60 sec/min
Q = flow, gallons per minute
C = calibrated coefficient of discharge (usually about 0.98)
A = area of entrance section where upstream manometer connection is made, square inches
g = acceleration of gravity (32.2 feet per second squared)
hj—h2 = difference in pressure between entrance section and throat, as indicated by manometer, feet
R = ratio of entrance to throat diameter = d/d, The pressures hj and h2 may be taken as illustrated in figure F-l for low pressures, or by a differential mercury manometer for high pressures. Gages may be used but will be less accurate.
(Courtesy of Fairbanks Morse, Inc., Pump Division)
(1) The flow from a pipe under pressure can be conveniently measured by installation of an orifice on the end of the pipe (fig. F-2), or by insertion of an orifice plate between two flanges in the pipe (fig. F-3). The pressure tap back of the orifice should be drilled at right angles to the inside of the pipe and should be perfectly smooth as illustrated in figure F-4. A rubber tube and glass or plastic pipe may be used to measure the pressure head. The diameter of the orifice plate should be accurate to 0.01 inch; the edge of the plate should be square and sharp, should have a thickness of У, inch, and should be chamfered at 45 degrees as shown in figure F-2. The approach pipe must be smooth, straight, and horizontal; it must flow full, and the orifice should be located at least eight pipe diameters from any valves or fittings. The flow for various sized cap orifice-pipe combinations can be obtained from figure F-5.
(2) The flow through an orifice in a pipe can be computed from
Q=CA2,—— у……………… x Z2gh (F-2)
VI – (d2/dj4
Q= capacity, cubic feet per second C = orifice discharge coefficient A2 = area of orifice, square feet d2 = orifice diameter, inches dt = pipe diameter, inches g = 32.2 feet per second squared h= pressure drop across the orifice in feet of head
(3) The expression Vl – (d2/dt)4 corrects for the velocity of approach. The reciprocal of this expression and the coefficient C are listed in the following tabulation for various values of d2/dj.
c, Pitot tube. The flow in a pipe flowing full can also be determined by measuring the velocity at different locations in the pipe with a pitot tube and differential manometer, and computing the flow. The velocity at any given point can be computed from
V = C v/2gh; (F-3)
v = velocity C = meter coefficient g = acceleration of gravity hv= velocity head
The flow is equal to the area of the pipe A times the average velocity V, or
Q = AV (F-3 a)
v = velocity at center of concentric rings of equal area
n = number of concentric rings
F-3. Approximate measurement methods.
a.Jet flow. Flow from a pipe can be determined approximately by measuring a point on the arc of the stream of water emerging from the pipe (fig. F-6), using the following equation:
Q = (F-4)
Q= flow, gallons per minute
A = area of stream of water at end of pipe in square inches. If the pipe is not flowing full, the value of A is the cross-sectional area of the water jet where it emerges from the pipe. The area of the stream can be obtained by multiplying the area of the pipe times the Effective Area Factor (EAF) in figure F-7 using the ratio of the freeboard to the inside diameter of the pipe.
x= distance along axis of the discharge pipe through which the stream of water moves from the end of the pipe to a point(s), inches
у = distance perpendicular to the axis of the discharge pipe through which the stream of water drops, measured from the top or surface of the stream of water to point(s), inches It should be noted that the x and y distances are measured from the top of the stream of water; if y is measured in the field from the top of the pipe, the pipe
thickness and freeboard must be subtracted from the measured y to obtain the correct value of y.
b. Fountain flow. The flow from a vertical pipe can be approximated by measuring the height of the use of the stream of water above the top of the pipe (fig. F-8). Two types of flow must be recognized when dealing with fountain flow. At low crest heights, the discharge has the character of weir flow, while at high crest heights the discharge has the character of jet flow. Intermediate values result in erratic flow with respect to the height of the crest H.
(1) Where the flow exhibits jet character, it can be computed from
Q = 5.68KDVH (F-5)
Q= flow, gallons, per minute K = constant varying from 0.87 to 0.97 for pipes 2 to 6 inches in diameter and h = 6 to 24 inches D = inside pipe diameter, inches H = vertical height of water jet, inches Where the flow exhibits weir character, it can be approximated by using the Francis Formula, Q = 3.33 Bh3’2, with В being the circumference of the pipe.
(2) Some values of fountain flow for various nominal pipe sizes and heights of crest are given in table F-l.