Work procedure

1. Fill in reservoir 1 with water. (Fig. 3.2).

2. Open faucet 4 approximately on 1/4 till 1/5 turnover and set up the minimum water rate.

3. After the water level in piezometers is set measure the piezometer heights for following resistances: gradual enlargement, gradual contraction, sudden enlargement, and sudden contraction.

4. By means of calibrated tank 6 measure the volume of water W and time T for its filing.

5. Calculate the rate Q and speed values V_av .

6. Calculate the values with formulas 3.4 or 3.5, choosing in each case larger value of a speed for particular local resistance.

7. Determine the coefficients by formulas 3.6 or 3.7, following item 6.

8. Close faucet 4, open faucet 5 on 1/4 till 1/5 turnover and set minimum water rate.

9. Repeat the procedures of items 3-5 for faucet local resistance.

10.Taking into account the inlet and outlet diameter of conduit calculate the difference of piezometers readings, find the particular local resistance at entrance and coefficient by formula 3.2.

11. The results of measurements and calculations put down into table3.2.

12. Make conclusions.

Table 3.2

Type of local resistsance	Smooth increasing	Smooth decreasing	Sudden increasing	Sudden decreasing	Faucet
Measured volume W,cm3
Time for tank filling T,s
Flow rate Q,cm3
Average speed Vav,cm/s
Local head losses hl,cm
Coefficient of local resistance l

Laboratory work 4 determination of discharge coefficients of liquid flow through orifices and mouthpieces Brief theoretical information

Liquid flow through orifices and mouthpieces is frequently considered in engineering field .It is typical for liquids that during discharge potential energy of liquid in reservoir transforms in kinetic energy with more or less losses. This phenomenon occurs very often in aircraft engineering. Liquid flow of different jets is also referred to as discharge through orifices or nozzles. Liquid flow through holes and nozzles requires determination of flowing speed and flow rate.

1. Discharge coefficients of liquid flow through an orifice in a thin wall.

An orifice in a thin wall is the hole where there are no energy losses in liquid flow due to viscous friction. Liquid flows towards the centre of the orifice due to inertia forces and simultaneously is carried by the stream along axis 0-0 (Fig. 4.1, 4.2).

Fig. 4.1. Flow through round orifices: a – in a thin wall, b - sharp edged hole

Fig. 4.2. Scheme of experimental system

Degree of fluid contraction is determined by the contraction coefficient , which equals relation of stream cross-section area to the area of the hole , .

The contraction coefficient essentially depends on the nature of contraction, which can be full or partial, complete and incomplete.

An incomplete contraction implies influence of the sides when the distance between orifice and sides is less then 3d. Contraction is partial if the directing side is near the orifice. The more discharge speed the greater the loss of pressure head H will be.

Bernoulli’s equation for liquid flow from its free surface in the reservoir (section 1-1 in Fig. 4.2) to the contracted cross-section (section 2-2), where it takes cylindrical shape, for even distribution of flow speeds is

,

where (V₂ =V_A) is actual discharge speed, is resistance coefficient.

In case under consideration p₁ = p₂ = p_at, and V₁ 0, so

or (4.1)

,

where is speed coefficient considering loss of pressure.

For ideal liquid , in this case  = 0, = 1.

Consequently, for the ideal liquid theoretical speed is equal to :

This formula is called Torichelli’s formula. So, coefficient is the relation of the real liquid discharge speed to the ideal liquid speed. It should be considered that distribution of speeds in the flow section is even only in the central part of the section.

The coefficient can be determined experimentally. Equations of motion are the following:

X = V_A t (4.2)

and

, (4.3)

where t - time; X, Y - co-ordinates of a particle (Fig. 4.2).

After combining 4.2 and 4.3 the equation of a particle motion stands for:

. (4.4)

Putting to the formula (4.4), one shall get:

. (4.5)

Liquid flow rate in the contracted section equals the product of actual discharge speed and actual flow cross-section area:

.

Putting one follows:

, (4.6)

where is the flow rate coefficient, Q_T is the theoretical flow rate of liquid.

Consequently, coefficient  is relation of the actual flow rate to the theoretical flow rate, which implies flow contraction and resistance losses.

Coefficients depend on the basic criterion of hydrodynamic similarity, the Re-number. Graphic dependence of coefficients and on Reynolds’ number for round orifices is shown in Fig. 4.3.

Fig. 4.3. Graphic of dependence , on the Reynolds’ number for round orifices in a thin wall

For liquids with low viscosity (water, benzene, kerosene and others) discharge usually corresponds with large Reynolds’ number that’s why discharge coefficient is being changed within small limits; through calculations their average values are usually of such size: = 0,63; = 0,97; = 0,61; = 0,065.

Discharge coefficients can be estimated experimentally as it is shown in Fig4.2.