Instruments for pressure measurement

Laboratory work № 4
DETERMINATION OF THE VENTURI TUBE
EXPENDITURE COEFFICIENT
1. General information
Venturi tubes (or Venturi) is the most common throttle device for measuring fluid flow in a pressure line. It consists of a short tube of variable cross-section, i.e. first tapering, and then expanding, inserted into the pipeline, as shown in Fig. 5.1.

Fig.5.1
The action of the Venturi tube is based on the law of conservation of energy during fluid motion, expressed by the Bernoulli equation. When a liquid passes from a wide section (ω₁) to a narrow (ω₂), the velocity v increases and, accordingly, the pressure or piezometric height decreases .
This is reflected by the readings of the piezometers connected to the wide part of the venturi and the neck. Due to the gradual narrowing and the long gradual expansion of the Venturi section, the flow of liquid flows through it without detaching from its walls, so that the pressure losses in the Venturi tube will be small and they can be neglected.
Then for the horizontal tube (z₁ = z₂) and taking approximately α₁ = α₂ = 1, the Bernoulli equation, referred to sections I-I and II-II, will be:

By the continuity equation the velocities are inversely proportional to the live cross sections
By introducing into the equation the difference of the piezometric head , expressing the speed v₁ through v₂, we get: . And the expense without taking into account losses, i.е. theoretical consumption
.
Value depends on the ratio of the diameters of the wide and narrow parts and is called the permanent Venturi. The actual liquid
flow rate will be less than theoretical, since in the real case the head losses and the coefficients of the nonuniformity of the velocity distribution (α₁, α₂) in the individual sections of the Venturi tube will be taken into account.
Then the actual flow of the venturi will be:

whence , where - coefficient of flow of the Venturi tube and fluctuates within 0,96÷0,99. As the velocity of the fluid increases, it also increases.
2. Purpose of laboratory work
Determine the coefficient of flow of the Venturi and calculate the flow of water in the pipeline at different indications of the piezometer. Construct a calibration curve for the given Venturi at different pressure differences .
3. The order of performance of work
Water using a centrifugal pump (1) (fig.5.2) from the receiving tank (2) is fed into the pipeline (3) where the venturi (4) is installed.

Fig.5.2
Then, with some opening of the gate valve on the pressure line, after the mercury level in the diffuser is established, reports are made on them and the difference h is calculated. The actual flow rate is measured using a flow meter
(5): , where W – the volume of water flowing through the system for a certain period of time τ, the duration of which is usually determined by the stopwatch. Installed 5-6 different water flows with the help of the gate valve (6), repeat all the necessary measurements and calculations.
All measurement and calculation data are recorded in the table on the basis of which the curve is plotted for the actual flow rate of fluid Q_d from the head difference .

№№	Indicators	Units	experiments
			1	2	3	4	5
1.	Diameter of wide part d1	sm
2.	Cross-sectional area ω1	sm^2
3	Throat Diameter d2	sm
4.	Cross-sectional area ω2	sm^2
5.	The volume of water passed through the counter W	sm^3
6.	The time of passage of the volume of water W through the counter τ	s
7.	Water flow rate Qд	sm^3/s
8.	Difference in indication h	sm.w.с.
9.	Theoretical expenditure Q	sm^3/s
10.	Flow coefficient	-

Laboratory work № 5
DETERMINATION OF THE HYDRAULIC RESISTANCE COEFFICIENT AT THE TURBULENT MOTION
1. General information


When fluid flows in the pipeline, some of the energy of the flow (hydraulic head) h_n is expended to overcome the hydraulic resistances. The latter can be of two types:

1) the resistance (friction) along the length (hl), which include energy losses on straight sections of the pipeline, at distances sufficiently remote (l = 40 ÷ 50d) from the entrance;
2) local resistance hm, i.e.
(1)
The study of hydraulic resistances is possible only in steady-state motion. When liquid flows in a straight pipe, the frictional pressure loss along the pipe length is determined by the Darcy-Weisbach formula:
, (2)
where λ – coefficient of hydraulic resistance along the length of the pipeline (2); l – pipe length; d – pipe diameter; v – average fluid velocity; g – acceleration of gravity.

The coefficient of resistance along the length depends on two dimensionless parameters: and The first of these parameters is the Reynolds number, and the second is the relative roughness, hence:

The nature of the effect of these two parameters on the resistance of natural rough pipes is seen in Fig. 6.1, which is constructed from the results of the experiments.

Fig.6.1

For hydraulically smooth pipes (δ> Δ). Numerous studies of turbulent motion have established that for Re = 2000 ÷ 80000 λ does not depend on the roughness, but depends only on Re, i.e. pipes, for which , are called hydraulically smooth. For large Re numbers, the resistance coefficient ceases to depend on Re, but depends only on the roughness, i.e. .
Pipes in which λ depends on the relative roughness are called quite rough pipes.
The area of ​​motion in which , is called transitional. In turbulent motion, λ is determined by empirical formulas. For hydraulically smooth pipes, the Blasius form
(3)
and Konakova
(4)
For the transition zone, when ,
the formula of A.D.Altshul is recommended:
(5)
For quite rough pipes - the formula of B.L.Shifrinson:
(6)
To investigate hydraulic resistance in the laboratory, an experimental circulating installation has been created (Fig. 6.2.)

Fig.6.2

2. Description of the installation

Figure 6.2. The scheme of the experimental setup is shown, which consists of an electric motor (1), a centrifugal pump (2). Pumping is carried out by the circulation cycle with the intake of water through the suction pipe (7) from the tank (10) and the return of the water passing through the discharge line (4) into the same tank.
The length of the working section of the pipeline (8) is l = 6 m. At the beginning and at the end of the section, holes are drilled in the pipe connected to the differential piezometer (9) by means of copper pipes. The flow rate is measured by a meter (5) or by means of a venturi (6), one revolution of which corresponds to 1 m3 of water volume. The speed of water movement in the pipe is regulated by a valve (3).
3. The order of the experiment.

The purpose of this paper is to determine the coefficient of hydraulic resistance (λ) experimentally and to construct a dependence curve. Including the pump, water from the tank is fed into the pipeline. Opening the valve (4), the corresponding mode is set.
Loss of head at the working section of the pipeline, i.е. along the length between sections 1-1 and 2-2 (see Fig. 2) is determined by the Bernoulli equation:


Since the pipe, horizontal , the diameter of the pipe changes over the entire length, i.e. d = const, therefore, and h_m = 0 and v₁ = v₂. Then Так как труба, горизонтальная , диаметр трубы меняется на всём протяжении, т.е. d = const, следовательно, и h_м = 0 и v₁ = v₂. Тогда
(7)
Loss of the head of the wound to the readings of the differential piezometer:
(8)
Observations are performed at least 4-5 times at different flow rates. During each experiment it is necessary to measure:
1. The meter reading (n) for the time τ, i.e. the volume (W) of leaking water, Which equals:
, m³ (9)
where n is the number of the counter; (0.1 m³ - water volume corresponds to one meter division);
2. Time τ by stopwatch;
3. Indication of the differential piezometer h_hg in mm.hg.c.;
4. Water temperature by thermometer.
When processing the measurement results, calculate:
1. Consumption
, (10)
2. Average flow rate in the pipeline
, (11)

3. Recalculation of the mercury column in the water column:
, m.w.c.

4. 
   The coefficient of hydraulic resistance along the length of the pipeline λ by formula (2)
   

(12)

and according to empirical formulas (3) – (6).
5. Kinematic viscosity at temperature
,

6. The Reynolds number (13)

6. 
   
   6. Calculate the coefficient λ by the formulas (3) and (6). The value of Re is taken from the calculated Re by the formula (13). For steel seamless pipes that have been in use Δ = 0,15 ÷ 0,3 mm, Δ_ср = 0,2 mm.
   
7. 
   On the basis of experimental data, the dependence curves
   
   
   
8. 
   with the application of experimental points, and points obtained in the calculation using formulas (3) and (6). Results to compare.
   

Preset values
1. The internal diameter of the pipe is d = 5.08 cm.
2. The length of the working section of the pipeline 1 = 6 m.
The results of the experimental and calculated data should be entered in the table.

№	Hydraulic parameters	The results obtained from the experiments
		1	2	3	4	5
1.	The volume of water that has flowed during the time τ. W, м^3
2.	Time of water flow τ, с
3.	Consumption of leaking water Q, м^3/с
4.	Average flow velocity in the pipe v, м/с
5.	Differential piezometer:hhg, m.hg.c