Method of determining hydraulic friction loss

FIELD: agriculture.

SUBSTANCE: method comprises modeling the process of interaction of water flow with a rough surface by changing the working member of the sloping chute for a precision member with the smooth surface, measuring the height of the water flow in the entrance and exit sections of the chute by means of micrometer with measuring needle, determining the flow rate, and measuring the width of the chute. The smooth member is changed for the working member provided with a rough surface, and the height of the water in the exit section of the chute is measured.

EFFECT: simplified method.

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The invention relates to agriculture, in particular to methods for the study of the flow of melt and rain waters arising on stationery surface (on the slopes, gully network in temporary streams and so on), and can be used in the field of hydrology, hydraulic engineering, reclamation, industrial, civil and road construction.

There is a method of determining the hydraulic friction losses, including the depth measurement of fluid flow by means of testera [2, s]with Vernier with a multiplier of 0.1 mm, and the liquid flow through the Weir Thomson [2, p.123].

Evaluation of hydraulic friction losses produced by the hydraulic resistance coefficient [2, s], which is determined using formula A. Darcy - Uwabaki

where λRthe hydraulic resistance coefficient; g - acceleration of gravity; R is the hydraulic radius; i - slope; V - velocity of water flow.

When designing hydraulic structures are usually encountered with quadratic resistance area, when the water flow has enough speed where you can apply the Chezy formula [4, s], using estimates of hydraulic friction loss coefficient Chezy

where C is the Chezy coefficient; V is the velocity of the Otok water; R is the hydraulic radius; i is the gradient of the slope.

To calculate the above ratios With and λRrecommended roughness coefficient n, proposed by Swiss engineers Eganville and Cattenom, the definition of which is possible on the table Langille-Cutter [4, s].

The disadvantage of this method is that when determining the parameters of fluid flow (flow rate, the height of the thread) it is necessary to establish uniform motion [2, s]; the use of empirical and semi-empirical formulae for determination of hydraulic resistance coefficient λRand Chezy coefficient C, the use of which is limited by the limits of the experiments on which they are based [2, p.123]; the use of the roughness coefficient n in table Langille-Cutter on the basis of purely descriptive (rather than quantitative) characteristics of the channel [4, s]; the coefficient of hydraulic resistance λRand the Chezy coefficient With values are not constant and depend on different parameters of stream and river channels [1, p.33].

The purpose of the invention is to simplify the method for determining the hydraulic friction losses.

This objective is achieved in that in the method of determining the hydraulic friction losses, including the modeling of the interaction process water stream with a rough surface, for which sportsouth the working part of the inclined trough, made in the form of precision fabricated sample with smooth and rough surface, measure the height of the water stream using a micrometer with gauge needle in the input and output parts of the tray, determine the water flow rate, measure the width of the tray, and the dimensionless figure ϕby which assess the hydraulic friction losses, is determined by the formula

where QIn- water consumption, m3/s; hg- the height of the water flow in the output of the tray when interacting with a smooth surface, m; hW- the height of the water flow in the output of the tray when interacting with a rough surface friction, m; hB1- the height of the water flow in the front part of the tray, m; width tray, m; g - gravitational acceleration, m/s2; z is the vertical coordinate between the centers of gravity flow in the cross section of flow in the input and output parts of the tray, M.

For explanation of formula (1) consider the flow of water in the tray with smooth surface friction (figure 1) and with a rough surface friction (figure 2). For one dimensional flow equation of continuity can be written

where Ux- the speed of the water in the tray on X.

Multiplying equation (2) Ω dx and integrating, we obtain the consumption of water in the tray

where Qinthe flow in the water in the tray; Ω - screening area flow; V is the average speed in the live section.

Equation (3) shows that at the steady state flow of water in the tray, despite the change in average velocity V and living areas-sections Ω the length of the stream, the flow rate Qinit remains constant.

Change in average speed can be determined from the following assumptions. Let the stream of the screening area d Ω speed on separate lines in the same current. Then the stream per unit of time is the amount of water

In hydrodynamics [4] under the average speed in the live section realise such a speed that should move all fluid particles in the flow to pass through his living section of the actual consumption. Therefore, for clarity, simultaneously with the actual flow consider a dummy stream, which all streams in the live section have the same velocity Ux. For a thread when Ux≡V equation (4) can integrate

Hence the expression to determine the average speed

From equations (3) and (5) we can obtain the dependence of

showing that the average speed is always inversely proportional to the squares of the ratios is ejstvujuschij living sections. So

where is the width of the tray; VinVg- the rate of flow of water respectively at the inlet (section 1-1) and output (section 2-2) parts tray; hinhg- the height of the water flow, respectively, on the input (section 1-1) and output (section 2-2) parts of the tray.

The mass of water flowing through the tray during t:

where ρin- the density of water.

The change in kinetic energy of the water in sections 1-1 and 2-2:

Expression (10) subject to (8) and (9) after some transformations will be copied

The change of total energy in sections 1-1 and 2-2

where z is the vertical coordinate between the centers of gravity flow in sections 1-1 and 2-2.

Consider the flow of water in the tray with a rough surface friction (figure 2).

The energy change of the water in the tray, respectively, in sections 1-1 and 2-2

where VB1VW- the rate of flow of water respectively at the inlet (section 1-1) and output (section 2-2) parts of the tray.

Because here consider the interaction of water flow with unyielding surface friction, there is reason to believe that

where mW, mB1the mass of water, flowing through the tray at time t.

As for the case in question

the expression (13) after some transformations takes the form

The change of total energy in sections 1-1 and 2-2

where z′ - the vertical coordinate between the centers of gravity flow in sections 1-1 and 2-2.

Dividing the expressions (12) and (17) on the gravity of the flowing water mWg=mgg=ρinQintg, obtain the formula for determining the change in the intensity of energy flow:

where agthe change in specific energy of the fluid flow in the interaction with a smooth surface, m; AndWthe change in specific energy of the fluid flow in the interaction with a rough surface friction, m

Experimental studies have shown that hin≈hB1z≈z′ at the same values of Qin.

Let us introduce the dimensionless figure ϕ:

Substituting expressions (18) and (19) (20) subject to hin≈hB1and z≈z′get the formula (1)

Evaluation of hydraulic friction losses based on specific values of the dimensionless figure ϕ may be sudestada as follows. From the expression (20) or (1) the desired value AndWequal to

and the magnitude of the pressure losses along the length on the smooth surface friction is determined by the formula [4, s]

where λgis the coefficient of hydraulic resistance on a smooth surface friction; lg- the length of the smooth friction surface, m; Vg- speed flow over a smooth friction surface, m/s; Rg- hydraulic radius, m In the formula (22) the change in specific energy of the fluid flow Andghas a dimension, expressed in units of length, and is equal in magnitude to the pressure losses along the length of the hl.

Then the expression (21) with (22) takes the form

where hl- the pressure loss along the length on a rough surface friction, m

In this case, to determine the pressure loss along the length on a rough surface friction hl=AWenough to know for hydraulically smooth friction surfaces of tabular data values λg[4, pp.163] and specified values of lgVg, Rg≈hgand the dimensionless figure ϕ.

Figure 3 shows a device for the implementation of the proposed method [3]; figure 4 - section a-a figure 3.

The device consists of an inclined tray 1 is fixed on the base 2 (Fig 3), the de tray is composed of three separate parts, consisting of input and output 3 made with hydraulically smooth surface (e.g. mirror glass), and working 4, made with the investigated rough surface, precision installed between the input and output parts with micrometer screws 5, placed in the base 2, 6 micrometers with measuring needles 7 installed in the input and output parts of the tray along its longitudinal axis on the side walls (figure 4), 8 corners, placed on the sides of the base along the entire length, ensuring the straightness of the tray 1. The device is equipped with a power supply system 9 constant pressure, the damper 10 and the clamp Hoffmann 11.

The method is implemented as follows. Before the beginning of experiments instead of the working part 4 in tray 1 set of precision fabricated sample with a hydraulically smooth surface (e.g. mirror glass), which lines the joint hydroisolyatsia (conventionally not shown). Then with the help of the power system constant head is set to the specified water flow rate QIn. Opens the clip Hoffman 11 and 6 micrometers with measuring needle 7 measured the height of the water flow in the input hB1and the output hgthe parts of the tray 1. The results obtained are recorded in the log of observations.

Then replace the glass in the tray 1 set working frequent the 4 with a rough surface. Junctions of the working part 4 and tray 1 waterproofed. Opens the clip Hoffman 11 and 6 micrometers with measuring needle 7, with the aforementioned method, measured the height of the flow of water (hinin the front part of the tray (as a result of research it was found that for the same set of cost stream height hin≈hB1so hinnot measured) and the height of the flow of water (hWthe output of the tray. The obtained data QInhin≈hB1hghWare substituted in the expression

where QIn- water consumption, m3/s; hg- the height of the water flow in the output of the tray when interacting with a smooth surface, m; hW- the height of the water flow in the output of the tray when interacting with a rough surface friction, m; hB1- the height of the water flow in the front part of the tray, m; width tray, m; g - gravitational acceleration, m/s2; z is the vertical coordinate between the centers of gravity flow in the cross section of flow in the input and output parts of the tray, M.

An example implementation of the method is given in the table. The fraction of particles of a specific average diameter d obtained using the sieve analysis of sand located on ancient alluvial deposits.

Sources of information

1. Grishanin C.V. Hydraulic resistance natural Ruse is/ Kvien. - SPb.: Gidrometeoizdat, 1992. - 180 S.

2. Zegzhda A.P. Hydraulic friction losses in ducts and pipes/ Apegga. - L.-M.: Gastrolyzer, 1957. - 278 S.

3. RF patent № 2021647, class. And 01 In 13/16, 1994.

4. Chugaev P.P. Hydraulics: Textbook for universities/ RPE. - SPb.: Energoizdat, 1982. - 672 S.

1. The method of determining the hydraulic friction losses, including the modeling of the interaction process water stream with a rough surface, the height measurement of fluid flow, characterized in that when carrying out experiments with smooth and rough surfaces using the inclined trough measure the height of the water stream using a micrometer with gauge needle in the input and output parts of the tray, determine the water flow rate, measure the width of the tray, and the dimensionless figure ϕby which assess the hydraulic friction losses, is determined by the formula

where Qin- water consumption, m3/s; hg- the height of the water flow in the output of the tray when interacting with a smooth surface, m; hW- the height of the water flow in the output of the tray when interacting with a rough surface friction, m; hB1- the height of the water flow in the front part of the tray, m; width tray, m; g - gravitational acceleration, m/s2; z - verticalalign between the centers of gravity flow in the cross section of flow in the input and output parts of the tray, m



 

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