Instruments for pressure measurement
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Laboratory work № 6 DEFINITION OF THE COEFFICIENT OF LOCAL HYDRAULIC RESISTANCE General information Local hydraulic resistances are created in sections of pipelines at which the flow rates vary in magnitude or direction as a result of changes in the size or shape of the pipe sections. Local losses are expressed in fractions of the high-speed head by the following expression: where ζ – coefficient of local resistance; v – speed after local resistance. The main types of local pressure losses can be conditionally divided into the following groups: 1. Losses associated with changing the cross-section of the flow (or its average velocity). This includes various cases of sudden or gradual expansion, narrowing the flow. 2. Losses caused by a change in the flow direction (angles, bends used on pipelines). 3. Losses associated with the flow of liquid through the valves of various types (valves, taps, check valves, grids, selections, throttle valves, etc.). 4. Losses associated with the separation of one part of the flow from another or the merger of two flows into one common. This includes, for example, tees, crosses and holes in the side walls of pipelines in the presence of transit flow. If local resistances are located sequentially at close distances, and in the separating section of the pipeline, the stabilization of the flow does not manage to occur, it is necessary to take into account the mutual influence of local resistances. The latter will affect the magnitude of total local losses, which may be greater or less than the sum of pressure losses in isolated local resistances. Thus, for example, when the two taps are connected in series (turning), the resistance coefficient ζсум ≈ 1,5ζо (where ζо is the resistance coefficient of the isolated tap). The coefficients of various local resistances are determined experimentally. Sometimes local head losses are expressed in the form of an equivalent length(leq) of a straight section of the pipeline, the friction resistance of which is equal in magnitude to that of the local pressure losses, i.e. using the conditions: , , or . The coefficient of hydraulic resistance λ, as is known, depends on the Reynolds number and the relative roughness, so the same value of the local resistance coefficient ζ generally corresponds to a different value of the equivalent length. Only in the quadratic region of resistance, when λ ≠ f (Re), the equivalent length of a given local resistance depends only on the relative roughness. When the fluid moves with small Reynolds numbers, the local resistance coefficients depend not only on the geometric characteristics of each local resistance, but also on the Reynolds number. In most cases, with increasing Re, the coefficient ζ decreases. The self-similarity (independence) of the coefficient ζ from Re for abrupt transitions occurs Re≥3,000, and for smooth transitions at Re≥100,000. В большинстве случаев с увеличением Re коэффициент ζ уменьшается. The self-similarity (independence) of the coefficient ζ from Re for abrupt transitions occurs Re≥3,000, and for smooth transitions at Re≥100,000. At very low Reynolds numbers, the flow of fluid through local resistances is continuous, head losses are caused by the direct action of viscous friction forces and are proportional to the speed in the first degree. The local resistance coefficients in this case depend on the Reynolds number and are determined by the dependence: where А – coefficient, depending on the type of local resistance and the degree of constraint of the flow (tab.1). The values of the coefficient A for some local resistances are given in Table 1. Table 1
With an increase in the Reynolds number, along with losses due to friction, head losses occur due to flow separation and the formation of vortices (the transition region of resistance). At sufficiently large Reynolds numbers, the losses in the vortex formation acquire the basic value, the pressure losses become proportional to the square of the velocity, since the coefficient ζ ceases to depend on the Reynolds number and is determined only by the flow geometry (the so-called quadratic or self-similar resistance region). For an approximate estimate of the coefficient of local resistance, we can use the formula of A.A. Altshul: where ζкв – coefficient of resistance in the self-similar region. ζ and Re are referred to the cross section of the pipeline. Description of the experimental setup to determine the coefficient of local resistance The general scheme of the experimental setup for studying local pressure losses is given in the figure (Fig. 7.1). Fig.7.1 The installation consists of an electric driven centrifugal pump (2) for supplying water to the installation, a pipeline (24) with a diameter of 5.08 cm, a length of 6 m and a meter for measuring flow (5). The pipeline has various local resistances: a turn (28), a gate (27), a crane (26) and a check valve (25). The distance between local resistances is 1.5 m. The plant is powered by a circulating cycle with water from the reservoir (14) and the return of the water passing through the system into the same tank. Differences in static forces in the pipelines where local resistances are installed are measured by differential piezometers (10), (11), (12), (13), and on the straight section by a differential piezometer (9). The flow rate is measured with the EV-50 meter, one rotation of which corresponds to 1 m3 of water volume. The speed of movement in the water pipe is regulated by a valve (4). 3. The order of the experiment. The purpose of this paper is to determine experimentally the coefficient of local resistance (ζ) and construct the dependence curve ζ = f(Re). Including the pump, water from the tank is fed into the pipeline (24). Opening the valve (4), the corresponding mode is set. The loss of pressure in each working section of the pipeline (before and after the local resistance) between sections A and B is determined by the Bernoulli equation: Since the pipe is horizontal - zА = zВ, the diameter of the pipes does not change over the entire length, i.e. d = const, hence следовательно vА = vВ. , where – the amount of losses in the i section of the pipeline in question: (6) where – loss of pressure to overcome local resistance; – loss of pressure on friction in the pipeline between sections A and B. So as the length of the section AB lAB = 1.5 m, it can be assumed that the head loss section A * B * is 4 times greater than in the section AB ( ). Therefore, formula (6) can be written as follows: . From here: . It is necessary to make 4 experiments at different water flow rates. During each experiment, measure: The volume of water (W) that has passed through the time τ, which is equal to Yüklə 1,67 Mb. Dostları ilə paylaş:
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