Work Procedure

1. Fill in reservoir 1 (Fig. 1.2) with water and wait until it is quieted.

2. Open smoothly faucet 5 and set low water rate that corresponds to laminar flow.

3. Open faucet 2 of the tank with coloured liquid.

4. Increase water flow rate by opening faucet 5 till oncoming of turbulent flow.

5. With calibrated tank 6 measure amount of water having been fed into the tank during period of time T fixed by a stop watch.

6. Put down the results of measurements in Table 1.1.

7. Measure water temperature and determine the coefficient of kinematic viscosity =(t), (see Appendix 1).

8. Determine High critical Reynolds’ number.

9. Set in the turbulent flow in pipe 4 by more opening of faucet 5.

10. Reduce water flow rate by smooth closing of faucet 5 and observe critical flow.

11. Follow the instructions of item 5 and 6.

12. Determine Low critical Reynolds’ number.

13. Determining the Re- numbers should be repeated 2-3 times. Compare the received results with mentioned above.

14. Draw conclusions.

Table 1.1

Number of measurement	1	2	3	4
Measured volume, cm3
Filling-Time, s
Water rate Q, cm3 /s
Flow Speed Vav, cm/s
Reynolds’ number, Re
Visual water flowing

Laboratory work 2

Determination of resistance coefficient

And pressure losses along a pipe line

Brief theoretical information

While flowing of viscous liquid along a pipe line part of the energy is being wasted to overcome liquid viscous resistance. In this case full flow energy decreases along the pipe line length. In general difference of full specific liquid energies in two pipe line cross-sections is equal to pressure losses between these sections:

Pressure loss for an invariable pipe line cross- section (Z₁ =Z₂ ) shows the difference of specific potential energies:

. (2.1)

At the same time, friction losses (or losses along pipe length) for an invariable length and diameter of the direct pipe line can be estimated by Darsi-Veihsbach`s formula:

, (2.2)

where  is a friction losses coefficient or coefficient of friction resistance; it can be considered as a coefficient of proportionality between pressure friction losses and product of relative pipe length by velocity head.

The experimental values of can be calculated by the formula, resulting from two equations (2.1) and (2.2):

. (2.3)

Experimentally (in general case) coefficient of resistance depends on character of the flow and conduit roughness. In laminar flow (Re< 2300) pipe roughness does not affect pressure losses and the coefficient of resistance can be calculated by the following formula:

. (2.4)

While conversing into turbulent flow (Re > 2300) firstly pipe roughness is buried in laminar sub-layer (Fig.2.1). With increasing of speed the sub-layer thickness decreases and roughness comes outwards (Fig.2.2). Evidently, the smaller the pipe roughness, the greater the critical Reynolds` number will be.

Fig.2.1 Fig.2.2

Consequently, there are “hydraulically smooth” pipes and “ rough or technical” pipes. “Hydraulically smooth” pipes imply small roughness, which does not affect coefficient of resistance in a turbulent flow. The coefficient depends only on Reynolds’ number and in 2300< Re< 100000 interval is calculated by fitted Blasiys’ formula:

(2.5)

or by Konakov’s formula for wider range of Reynolds’ numbers (2300< Re< 1000000):

. (2.6)

Seamless ferrous and non-ferrous pipes used in fuel, hydraulic, oil and pneumatic aircraft systems can be considered as “hydraulically smooth” and calculations should be done by those, mentioned above, formulas. Welded steel, cast-iron and cement pipes are referred to as "technical" and above stated formulas are not applicable to them, because resistance coefficient depends not only on Reynold’s number but on roughness, as well. So, it is significant not an absolute roughness but the relation of roughness size to the pipe radius, that is the relative roughness. The influence of Reynolds’ number and relative roughness on pipes resistance is distinctly visible on graphic, the results of I.I.Nikuradze’s experiments (Fig. 2.3). Experimental dependence =(Re) is universal for whole liquids of aircraft systems.

Fig.2.3. Dependence  on Re for pipes with artificial roughness, based on I.I.Nikuradze’s experiments

For practical calculations (while determining the resistance coefficient) for real rough pipes the following universal formula after A.D.Altshul should be used :

, (2.7)

where d is pipe diameter; is absolute roughness.

For hydraulic pipes maximum size of is the following: glass pipes - 0,0; seamless brass, lead, copper pipes - 0,0; seamless steel pipes - 0,0006-0,002; steel pipes - 0,003-0,01.

If << 7, formula (2.7) is changed to Konakov’s formula (2.6) for smooth pipes. If >>7, it is changed to the formula for fully rough pipes (for quadratic resistance):

. (2.8)

Friction losses in laminar flow increase in proportion to speed (and the flow rate). While conversing into turbulent flow resistance increases and then its value grows steeply by the curve similar to a parabola of the second degree (Fig. 2.4).

Fig. 2.4. Graphic of dependence of pressure loss on speed

For experimental determination of the resistance coefficient in this laboratory work two testing systems are used. Their principal schemes are similar and one of them is shown in Fig. 2.5. Systems operate with different liquids: with AMG-10 oil and water. Difference in liquid viscosity allows us to receive an experimental dependence =(Re) on wide range of Reynolds’ numbers starting from small numbers such as 20-50 to large ones as 20000.

The experimental systems consist of the following parts: feed-tank 1, testing pipe 3 and calibrated tank 5. The pressure losses in the pipe between two cross-sections are determined with two piezometers 2, (Fig.2.5). The liquid flow speed is being regulated with faucet 4.

Fig.2.5. Principal installation scheme for determination of resistance coefficient