Instruments for pressure measurement

hw, m.w.c
6.	The coefficient of hydraulic resistance, determined experimentally, λэксп
7.	Reynolds number, Re
8.	The coefficient of hydraulic resistance, calculated by the formula of Konakova, λК
9.	The coefficient of hydraulic resistance, calculated by the formula of Blasius, λБ

DETERMINATION OF THE HYDRAULIC RESISTANCE COEFFICIENT AT THE TURBULENT MOTION
1. 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.)
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 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 (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) 7. 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.
8. On the basis of experimental data, the dependence curves


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, sec
3.	Consumption of leaking water Q, м^3/sec
4.	Average flow velocity in the pipe v, м/sec
5.	Differential piezometer:hhg, m.hg.c