Venturi MetersThe measurement, using a Venturi meter, of incompressible liquids flowing down a pipe View other versions (5) Contents 1. Introduction 2. Measurement Of Flow. 3. Worked Examples 4. Vertical Venturi Meters. 5. Worked Example 6. Page Comments Introduction Venturi Meter are used to measure the velocity of flow of fluids in a pipe. They consist of a short length of pipe shaped like a vena contracta, which fits into a normal pipe-line Venturi Meters have the following characteristics:• Theoretically • They • The there is no restriction to the flow down the pipe. can be manufactured to fit any required pipe size. temperature and pressure within the pipe does not affect the are no moving parts. meter or its accuracy. • There • Unfortunately the accurate shape required of the inside of the meter makes them relatively expensive to manufacture. the quantity flowing is given by:(1) For the proof of the above equation please click on the red button (2) Applying Bernoulli's equation at stations 1 and 2 (3) (4) . For a meter with the above arrangements of manometers. Measurement Of Flow. (5) (6) (7) where (8) (9) Which can be written as (10) In practice. . A coefficient of discharge is therefore introduced. because of fluid resistance. the actual velocity and consequently actual discharge is LESS than that given by the above equations.96 to 0.99. which usually lies between 0. For the above arrangement the Quantity flowing is given by. This is achieved as shown in the following diagram. A more practical arrangement is to measure the difference in pressure rather than the absolute values. (11) Where the constant K is specific to a particular meter and will include an allowance for a coefficient of discharge.In an actual meter it is not be practical for the tubes to be taken straight up as shown. To see the proof of the above equation please click on the red button (12) (13) (14) (15) (16) (17) For any given meter this can be written as (18) . since the pressures would require the use of long tubes. Part 1) which it may be used. for the meter is 0.Worked Examples The solutions to the following examples have been hidden. one with no losses (19) Re-writing the equation . Take the specific weight of the liquid as and atmospheric pressure To see the solution please click on the red button Applying Bernoulli to an ideal horizontal Venturi meter. pipe-line. i. The pressure at the entrance to the meter is gauge and it is undesirable that the pressure should at any point. They can be seen by clicking on the red button. diameter throat is installed in a 6 in.96 find the maximum flow for (B.e. Example 1 A venturi meter with a 3 in. fall below Assuming that absolute.Sc. below the meter. and at 60 ft.(20) The quantity of fluid flowing along the pipe (Q)is given by:(21) (22) From equations (20) and (22) (23) (24) Thus for an Ideal meter:- (25) For the actual meter taking into account the of 0. diameter pipe 200 ft. of . of water (gauge) is maintained at the pipe inlet. of water and the absolute pressure at the meter throat is not to fall below 10 ft. A constant head of 70 ft.long. at the output of which is fitted a horizontal venturi meter having a throat diameter of 6 in. which is .96 (26) Example 2 Water is discharged from a pit through a 9 in. If the barometric pressure corresponds to 34 ft. The specific gravity of mercury =13.6 (B. for the pipe. It can also be seen that at the Datum the Potential Energy is zero and so substituting in given values to the above equation:- (28) (29) .Sc. Applying Bernoulli at A and B (27) As the pipe is of constant cross section there can be no change in velocity between A and B. find the maximum discharge that may be permitted. Part 1) To see the solution please click on the red button. the connecting tubes above the mercury being full of water. Under these conditions what would be the difference of level between two columns of a U-tube mercury manometer connected between the inlet and throat of the venturi meter.water. As a result H. The above equation can be therefore written in absolute form as:- (31) The head in the Venturi meter throat must not fall below 10 ft. of water absolute.(30) The pressure at A was given 70 ft. gauge which means that it was measured above atmospheric pressure which was 34 ft.the reduction in head in the throat of the meter is given by - (32) (33) (34) (35) (36) (37) . which may be assumed to be constant. . Neglect all other losses. The loss in the valve when fully open is 5 times the velocity head. for the meter is 0. The pipe is 4000 ft.97 and all the losses may be assumed to occur in the convergent portion.Sc. If the pressure at the venturi throat is not to drop more than 10 ft. long and f=0. what is the minimum throat diameter permissible. near to the entrance to the lower reservoir and 2 ft. The difference in levels of the reservoirs is 50 ft.(38) (39) (40) If the difference in Mercury levels is h (41) (42) Example 3 The flow of water in a 9 in. below atmosphere. above the level thereof. Part 2) To see the solution please click on the red button.006. (B. pipe connecting two reservoirs is measured by means of a venturi meter situated upstream of a regulating valve. Applying Bernoulli between the entrance and throat of the Venturi - (43) Where is the loss of head in the convergent portion of the venturi. (44) (45) (46) . (47) If there was no head lost in the venturi ideal inlet velocity as :(48) From equation (47) would be zero and writing the (49) Substituting this value for into equation (48) (50) Combining equations (49) and (50) (51) Substituting the above equation into equation (47) (52) (53) Substituting in values . Then applying Bernoulli to the whole pipe length:- (56) (57) Bernoulli is now applied between the water surface of the upper reservoir and the throat of the Venturi meter.(54) (55) Let be the head lost due to pipe friction between A and B and let be the head lost in the valve. (58) (59) (60) Dividing equation (60) by (57) (61) . It will be found that the formulae which have already been proved are equally applicable to vertical meters.(62) From which (63) Since (64) Vertical Venturi Meters. All the examples above and the theory have examined horizontal meters. . The following section considers a meter mounted in the vertical. if its relative density relative to water is 0.8 and the difference of level of the mercury columns is 7 in.Sc. If the mains diameter is in. and the throat diameter in.96 (B.6 and the meter coefficient as 0. Part1) To see the solution please click on the red button .Worked Example The following example is of a non-horizontal meter Example 4 A Venturi meter is connected at the main and throat sections by tubes filled with the fluid being metered by a differential mercury manometer. Use a direct application of Bernoulli's theorem taking the relative density of mercury to water as 13./hr. Prove that for any flow the reading is unaffected by the slope of the meter. calculate the flow of fuel oil in gals. Applying Bernoulli (71) (72) But for a given flow and are constant (73) Now the pressures at level XX .- (74) (75) From equations (73) and (75) . then. in the U-tube are equal and if the subscript m refers to mercury. (76) Now (77) (78) From equations (76) and (78) and substituting values (79) From which (80) (81) (82) .