Work procedure

1. Fill in reservoir 1 with water (Fig. 4.2).

2 Quickly open the cap of one of the tank mouthpieces and simultaneously put a calibrating tank 4 under the flow stream.

3. Open the faucet to fill the tank 1 with water and fix water level H.

4. Measure time T and volume of water W filling the calibrating tank.

5. Determine actual and theoretical flow rate and discharge coefficient .

6. Find resistance coefficient .

7. The results of measurements and calculations should be put down in table 4.2.

8. Repeat the procedures for two mouthpieces installed in tank 1.

Table 4.2

Type of nozzle	Internal		External
Pressure head H, cm
Time for filling the calibrating- tank T, s
Measured volume W, cm3
Actual flow rate , cm3/s
Theoretical flow rate , cm3/s
Discharge Coefficient
Resistance Coefficient

Laboratory work 5

Ventury flow meter as an example of engineering application of bernulli ‘s equiation Brief theoretical information

Bernoulli’s equation for two cross-sections of real (viscous) liquid flow:

, (5.1)

where indexes 1 and 2 correspond to sections 1-1 and 2-2 in Fig. 5.1;

Z is specific position energy of flowing liquid; is specific pressure energy; is specific kinetic energy of liquid ; is Coriolis’ coefficient of speed distribution ; is total loss of specific energy (pressure) between sections 1-1 and 2-2.

Fig. 5.1. Diagrammatic representation oа Bernoulli’s equation for real flow

Bernoulli’s equation for viscous flow is an equation of energy balance. Stream wise diminution of specific liquid energy per length unit is called hydraulic gradient. Change of specific potential (Z+P/g) energy per length unit is called hydrostatic gradient, and P/pg is called piezometric gradient.

Bernoulli’s equation is a basic principle of liquid flow. It allows understerding the operation of Venturi flow meters.

Venturi devices used for measurements include flow meter diaphragm 2, flow meter nozzle 3 and Venturi pipe 4 (Fig.5.2). These devices are widely spread owing to absence of moving parts, which makes them simple and reliable.

These devices operation is based on relation of liquid flow rate and pressure in two cross- sections.

Venturi Flow meter (pipe) consists of two conic branch pipes of different length (Fig.5.2), turned to each other by their tops.

Fig.5.2.Scheme of experimental system

Determining equation of continuity with Bernoulli’s equation for cross-section 1-1 and 2-2 (formula 5.1)

and ,

we will get: ,

where ; is cross-section (1-1) area; is cross-section of Venturi device throat (2-2); Q_T is flow rate.

Consequently, pressure differential H for this flow meter depends only on its flow rate. Marking

,

we get

, (5.2.)

where is flow rate coefficient, depending on geometrical form of narrowing device and Reynolds’ number.

Taking , we get .

Existing theoretical methods for determination of this coefficient do not cover all factors affecting its value.

Therefore dependence Q on H is determined by measuring the flow rate values Q_r with calibrated tank and different pressure differentials H for several points of measuring. The graphical diagram then shows the relation between the flow rate and the pressure differentials.

Head loss in Venturi meter is to be calculated by formula:

,

where v is speed value at the outlet of the tube; is the resistance coefficient.

Incidentally, a diffuser is not essential for flow measurement, and a flow nozzle alone placed inside a pipe or between flanges can be used. In this case the convergence of the flow is gradual, as in the case of a Venturi meter, but the divergence beyond the nozzle is abrupt and eddies are being formed. The resistance of a flow nozzle is greater than that of a Venturi meter with a diffuser.

Another instrument for measuring fluid flow is an orifice meter . Owing to additional compression experienced by the fluid, the stream is nar­rowest a bit downstream from the orifice and its diameter is slightly less than the orifice diameter.

Diaphragm 2 (Fig. 5.2) is a ring disk with a sharp edge at an exterior side of the hole.

Nozzle 3 is made in a thick wall by drilling and another rounding of its side by radius, which is equal to wall thickness.

Flow rate through diaphragms and nozzles is determined by formula 5.2 for Venturi’s flow meter. Diminution of the actual rate comparising to theoretical in this case occurs due to the flow contracting effect, which is being hold in Venturi’s pipe.

For relatively small rate and low viscosity the flow rate coefficient can be taken as permanent.

Theoretical flow rate for nozzle and diaphragm is designed as:

,

where is a nozzle or a diaphragm cross- section area.

Flow meters are set as a rule, on a straight pipe line so that the pipe length should not be less then ten diameters before the device and not less than five diameters after it.