Venturi Meters

The measurement, using a Venturi meter, of incompressible

liquids flowing down a pipe

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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 there is no restriction to the flow down the pipe.

← They can be manufactured to fit any required pipe size.

← The temperature and pressure within the pipe does not affect the

meter or its accuracy.

← There are no moving parts.

← Unfortunately the accurate shape required of the inside of the meter

makes them relatively expensive to manufacture.

Measurement Of Flow.

For a meter with the above arrangements of manometers, 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)

(5)

(6)

(7)

where

(8)

(9)

Which can be written as

(10)

In practice, because of fluid resistance, the actual velocity and

consequently actual discharge is LESS than that given by the above

equations. A coefficient of discharge is therefore introduced, which usually

lies between 0.96 to 0.99.

In an actual meter it is not be practical for the tubes to be taken straight up

as shown, since the pressures would require the use of long tubes. A more

practical arrangement is to measure the difference in pressure rather than

the absolute values. This is achieved as shown in the following diagram.

For the above arrangement the Quantity flowing is given by.

(11)

Where the constant K is specific to a particular meter and will include an

allowance for a coefficient of discharge.

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)

Worked Examples

The solutions to the following examples have been hidden. They can be

seen by clicking on the red button.

Example 1

A venturi meter with a 3 in. diameter throat is installed in a 6 in.

pipe-line. The pressure at the entrance to the meter is

gauge and it is undesirable that the pressure should at any point,

fall below absolute.

Assuming that for the meter is 0.96 find the maximum flow for

which it may be used. Take the specific weight of the liquid as

and atmospheric pressure (B.Sc. Part 1)

To see the solution please click on the red button

Applying Bernoulli to an ideal horizontal Venturi meter, i.e. one with no

losses

(19)

Re-writing the equation

(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 0.96

(26)

Example 2

Water is discharged from a pit through a 9 in. diameter pipe 200

ft.long, at the output of which is fitted a horizontal venturi meter

having a throat diameter of 6 in. and . A constant head

of 70 ft. of water (gauge) is maintained at the pipe inlet, which is

at 60 ft. below the meter.

If the barometric pressure corresponds to 34 ft. of water and the

absolute pressure at the meter throat is not to fall below 10 ft. of

water, find the maximum discharge that may be permitted.

for the pipe.

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, the connecting

tubes above the mercury being full of water. The specific gravity

of mercury =13.6 (B.Sc. Part 1)

To see the solution please click on the red button.

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. 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)

(30)

The pressure at A was given 70 ft. gauge which means that it was

measured above atmospheric pressure which was 34 ft. 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. As a result H,the reduction in head in the throat of the meter is

given by -

(32)

(33)

(34)

(35)

(36)

(37)

(38)

(39)

(40)

If the difference in Mercury levels is h

(41)

(42)

Example 3

The flow of water in a 9 in. pipe connecting two reservoirs is

measured by means of a venturi meter situated upstream of a

regulating valve, near to the entrance to the lower reservoir and 2

ft. above the level thereof. The pipe is 4000 ft. long and f=0.006.

The difference in levels of the reservoirs is 50 ft. which may be

assumed to be constant. for the meter is 0.97 and all the losses

may be assumed to occur in the convergent portion. The loss in

the valve when fully open is 5 times the velocity head. Neglect all

other losses.

If the pressure at the venturi throat is not to drop more than 10 ft.

below atmosphere, what is the minimum throat diameter

permissible. (B.Sc. Part 2)

To see the solution please click on the red button.

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 would be zero and writing the

ideal inlet velocity as :-

(48)

From equation (47)

(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

(54)

(55)

Let be the head lost due to pipe friction between A and B and let be

the head lost in the valve. 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.

(58)

(59)

(60)

Dividing equation (60) by (57)

(61)

(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. It will be

found that the formulae which have already been proved are equally

applicable to vertical meters.

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. Prove that for any flow the reading is unaffected by

the slope of the meter.

If the mains diameter is in. and the throat diameter in.

calculate the flow of fuel oil in gals./hr. if its relative density

relative to water is 0.8 and the difference of level of the mercury

columns is 7 in.

Use a direct application of Bernoulli's theorem taking the relative

density of mercury to water as 13.6 and the meter coefficient as

0.96 (B.Sc. Part1)

To see the solution please click on the red button

Applying Bernoulli

(71)

(72)

But for a given flow and are constant

(73)

Now the pressures at level XX , in the U-tube are equal and if the subscript

m refers to mercury, then;-

(74)

(75)

From equations (73) and (75)

(76)

Now

(77)

(78)

From equations (76) and (78) and substituting values

(79)

From which

(80)

(81)

(82)