Instruments for pressure measurement

4. The results of observations and calculations are recorded in a table

№

Piezometer

Mercury Differential Pressure Meter

Δp

δ, %

Spring manometer

Δp

δ, %

Head (Pressure) m.w.c.

N/m^2

Head (Pressure) mm.m.c.

N/m^2

kq/sm^2

Pа

Laboratory work № 2
MODES OF MOTION OF THE LIQUID
1. General information

In 1883, the English scientist Reynolds found that there are two modes of fluid motion: laminar and turbulent. In the laminar regime, the flow of the fluid moves in separate streams and layers, and the trajectories of the individual particles do not intersect each other, i.e. the existence of a laminated flow or, as it is usually called, a laminar flow (from the Latin "lamina" - a layer) is established.
In the turbulent flow regime, the flow of the flow is disturbed, all the streams are mixed, and the trajectories often acquire a complex shape, intersecting with each other. The laminar motion regime occurs most often when moving through pipes of a liquid with a high viscosity (oil, petroleum products, clay, etc.), and also when water moves in capillary tubes and soil pores. Turbulent regime occurs in most cases when moving through pipes of low-viscosity liquids (water movement in pipes, channels, etc.). The study of laminar and turbulent regimes of motion is of particular interest, since the loss of specific energy (pressure loss) depends essentially on the regime of motion of the fluid.
It has been established by experiments that the transition of fluid motion from one regime to another is characterized by a definite value of the dimensionless complex, which is called the Reynolds number. The Reynolds number is the ratio of inertia forces to viscous forces (where – volume, S – area) and is expressed by the formula:
,
where ρ – fluid density; μ – dynamic viscosity coefficient of a liquid; V –
characteristic flow rate; l – characteristic linear flow size. As (ν – kinematic viscosity of a liquid), then the Reynolds number is written as:
If the pipeline has a circular cross-section, then the diameter d is usually taken as l, and the mean velocity over the section as v is assumed.
Then for a pressure pipe of circular cross section the Reynolds number has the form .
As can be seen from the formula, the number Re for a given fluid (ν = const) and a given pipeline (d = const) can vary due to a change in the average flow velocity v.
If in the pipeline to increase the speed v from zero, then at first laminar flow will be observed. At a certain flow velocity, called critical, the laminar regime changes to turbulent. The corresponding Reynolds number is called the critical Reynolds number and is denoted by Re_kr. According to the experimental data, the critical Reynolds number for the pressure motion in round tubes is assumed to be equal to Re_кr=2320, and for open flows and for the flow of non-circular flow Re_кр= =580. Thus, when Re < 2320 in the pipe there will be a steady laminar flow. With numbers Re> 2320 turbulent flow begins. Loss of head h_l along the length of the pipe with laminar motion is proportional to the first degree of speed: ,where К₁ – coefficient of proportionality, depending on the size of the pipe and the properties of the liquid.
In the turbulent mode of motion, the head loss depends on the speed in the degree n varying from 1.75 to 2:

where К₂ – coefficient of proportionality.
2. Objective
Establish an experienced way of having two modes of motion. Determine the Reynolds number for both modes. Mark the transition from laminar to turbulent and calculate the value Re_кr.
3. Description of the installation.

Fig.3.1
The installation (Fig. 3.1) consists of a rotameter 3, the liquid comes from the water pipe 1 through the valve 2. From the rotameter, the liquid flows through the pipe 5 to the glass tube 6 with a diameter d=2,5 sm.
It consists of a conical glass tube in which a float is placed with a constant cross section, and this float can move in a vertical direction, thereby changing the annular area of ​​the passage between the float and the walls of the tube.
Increasing the flow rate causes the float to occupy a position in the tube that corresponds to a larger flow area. Knowing the height of the float lift or the number of scale division, the calibration curve determines the flow rate of the liquid on the installation.
4.The order of the work.

1. Slightly opening the valve 2, starting from the full closing position, set a small average velocity of the liquid in the glass tube 6.

2. To demonstrate the fluid flow regimes, with a slight increase in pressure, evenly pressing the membrane, a colored trickle enters the stream. In laminar mode, the colored trickle does not mix with the bulk of the water, moves in layers or separately in the form of a colored trickle.
3. Having established the laminar flow regime of the liquid in the glass tube, the number of the rotameter division differs simultaneously.
4. Increasing the degree of opening of valve 2, perform several experiments with laminar driving.
5. Increasing gradually the opening of the valve and observing the behavior of the colored trickle, determine the moment when the laminar regime changes to turbulent. The transition moment is characterized by pulsation of the colored trickle, its disintegration and mixing with the rest of the fluid mass.
6. Opening the valve 2 further achieve a stable turbulent regime with intensive mixing of the colored liquid with water.
5.Calculation of the results of the experiment.
1. Measuring the temperature of the liquid, determine the coefficient of kinematic viscosity by the Poiseuille formula.
, sm²/sec
where t – water temperature, в ⁰С.
2. On the scale of the rotameter and the graph, the volume flow of liquid through the pipe is determined for all the experiments.
3. By the flow rate and cross-sectional area, the average velocity of the liquid in the glass tube is calculated. .
4. For each experiment, the Reynolds number is determined .
6. The results of the calculations are recorded in the table.

№№ п/п	Hydraulic parameters	Units	Experiences
			1	2	3	4	5
1	Number of scale divisions of a rotameter n
2	Volumetric flow Q	sm^3
3	Cross-sectional area pipes ω	sm^2
4	Average fluid velocity in the pipev	sm/sec
5	Water temperature t	^0С
6	Kinematic viscosity ν	sm^2/sec
7	Reynolds number Re
8	Fluid flow regime		lam	lam	trans	turb	turb

Laboratory work № 3
EXPERIMENTAL RESEARCHES OF THE BERNULLY EQUATION

1. 
   General information
   

The Bernoulli equation is the basic equation of hydrodynamics and shows the change in the kinetic energy of the volume of the fluid in question, referred to a unit of weight, by some of its displacement under the action of the applied external and internal forces on the same displacement per unit time. In other words, the Bernoulli equation is an analytical expression for the law of conservation of energy in the case of ideal fluid motion and the energy balance equation for the motion of a real fluid. For a trickle of an ideal fluid, the Bernoulli equation has the form:
(along the trickle, the terms of the equation have a linear dimension)
– geometric head or geometric height - the height of the position of the considered live section of the trickle over an arbitrarily chosen horizontal reference plane;
– piezometric head or piezometric height - the height at which the liquid rises in a piezometric tube installed perpendicular to the streamline under the action of hydrodynamic pressure in the considered live section of the trickle;
– velocity head or velocity height is the height to which the fluid rises, launched vertically upwards with an initial speed equal to the speed of movement in the stream section under consideration.;
High altitude can be measured by means of a Pitot tube, which is a piezometer with a bent at 900 and a drawn bottom end, which is fixed at the considered point of the section strictly against the flow of the trickle.
The sum of three members is the total head and is the elevation of the pressure line above the plane of comparison. The energy interpretation of the terms of the Bernoulli equation is accordingly the following:
- the total specific energy of the cross section of the moving fluid;
- the specific potential energy of the position of the section under consideration;
- the specific potential energy of the pressure of the section under consideration;
- the specific kinetic energy of the cross section under consideration.
For the flow of a real liquid, the Bernoulli equation has the form: ,
where v₁ and v₂ –average velocities in I and II of the flow sections considered, respectively; α₁ and α₂ – Coriolis coefficient in the corresponding sections of the flow.
The Coriolis coefficient α is the ratio of the actual kinetic energy calculated from the local velocities of the flow section in question and the kinetic energy calculated from the average velocity of the same cross section. Therefore, α depends on the degree of unevenness of the velocity distribution in the cross section under consideration, i.e. with laminar motion α = 2, but in a turbulent flow α = 1,0 ÷ 1,1.
Purpose of work: on a pressure horizontal pipeline of variable cross-section, trace through the devices the transfer of the potential energy of the flow into kinetic energy and back, in accordance with the Bernoulli equation. Calculate the total head in all sections and the head loss between sections.
According to experimental data, construct lines of piezometric and full head along the length of the stream.
и

2. 
   Description of the installation
   

The experimental stand (fig.4.1) consists of a variable section (d1 = d3 = 2.2 sm, d2 = 1.2 sm) connected to the water pipe and a horizontally installed glass pipe (1) and a pre-calibrated rotameter (2) for flow measurement.

Fig.4.1
In six sections along the length of the pipe, pressure tubes are installed: in the first section, a Pitot tube, and in the other sections piezometric tubes.
4. The order of the experiment

1. 
   The valves (3) and (4) are opened on the water supply line. Air is removed from the piezometers.
   
2. 
   By adjusting the valve (3), the required position of the float in the rotameter is achieved.
   
3. 
   The value of the volumetric flow Q in the system under consideration (tube 1) is determined from the altitude of the float's lift, according to the calibration schedule of the rotameter.
   

4. When the flow rate Q is set, the Pitot tube and piezometric tubes are recorded.
4. Processing the results of the experiment
1. The areas of the considered living sections of the flow are counted.
2. The average flow velocity in these sections is determined by the formula:
(1)
3. The flow regime is determined by equation
(2)

3. 
   Corresponding to the mode of motion with respect to the average velocities , the velocity head in all sections is calculated.
   
4. 
   According to the formula
   

(3)
the values ​​of the total head H and the piezometric head in all sections are determined.

5. 
   The head loss is calculated between the sections
   

(4)

6. 
   From the values ​​obtained and h
   

On a millimeter paper lines of a full and piezometric pressure on a length of a stream, giving a visual representation of the redistribution of energy with a change in the live cross-section along the flow according to the Bernoulli equation.
Protocol of work

№№	Indicators	Unit measurements	cross-sections
			1	2	3	4	5	6
1.	Cross-sectional area, ω	sm^2
2.	The height of the float in the rotameter, h	sm
3.	Water flow rate, Q	sm^3/sec
4.	average speed, v	sm/sec
5.	Traffic mode, Re
6.	Speed ​​head,	sm
7.	Pitot tube readings, Н	sm
8.	Piezometric head,	sm
9.	The total specific energy of the stream,	sm
10.	Loss of energy between sections, hп	sm