CodeCogs

The measurement, using a Venturi meter, of incompressible liquids flowing down a pipe

You're viewing an older version of this page (#3574). View the current version.

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

Blank

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:-

$\text{Quantity}=K\sqrt{H}$

(10)

For the proof of the above equation please click on the red button

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.

Blank

For the above arrangement the Quantity flowing is given by.

$\text{Q}=K\sqrt{h_1-h_2}$

(11)

Where the constant K is specific to a particular meter and will include an allowance for a coefficient of discharge.

Blank

To see the proof of the above equation please click on the red button

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 $10\;lb./in^2$ gauge and it is undesirable that the pressure should at any point, fall below $8\;lb./in^2$ absolute.

Assuming that $C_d$ for the meter is 0.96 find the maximum flow for which it may be used. Take the specific weight of the liquid as $60\;lb./ft.^3$ and atmospheric pressure $14.7\;lb./in^2$ (B.Sc. Part 1)

Blank

To see the solution please click on the red button

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 $C_d=0.96$ . 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. $f=0.007$ 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)

Blank

To see the solution please click on the red button.

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. $C_d$ 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)

Blank

To see the solution please click on the red button.

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.

Blank

More...

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 $3\tfrac{1}{2}$ in. and the throat diameter $1\tfrac{1}{4}$ 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)

Blank

To see the solution please click on the red button

Blank