MINISTRY OF EDUCATION AND SCIENCE OF UKRAINE

National Aviation University engineering mechanics of liquid and gas

Laboratory Works for Students of

Speciality 6.092100 “Industrial and civil building”

Kyiv 2002

УДК 629.7.064.3

ББК 0565 Я 73-5

Г464

Reviewer: PhD, prof. Valentine V. Garaga (Kyiv, NAU).

English language consultant: lecturer Margarita V. Karpenko (Kyiv, NAU).

Authors: Victor P. Bocharov, Vladimir S. Boutko.

Approved by the NAU drafting committee 26.06.2001.

Г464	HYDRAULICS. Methodical instructions on performance of laboratory works. Authors: V.P.Bocharov ,V.S. Boutko. – K: 2002. - 40p.

Laboratory works on "HYDRAULICS" contain brief theoretical information, description of experimental systems, general methodical instructions, laboratory work procedures and testing results.

Designed for students of NAU speciality 7.100106 “Production, technical maintenance and repair of aircraft and engines”.

ГІДРАВЛІКА. Методичні вказівки до виконання лабораторних робіт (англійською мовою). Укладачі: В.П. Бочаров, В.С. Бутько. – К.: НАУ, 2002.- 40с.

Лабораторні роботи містять короткі теоретичні відомості, опис експериментальних систем, загальні методичні вказівки, порядок виконання лабораторних робіт.

Призначені для студентів спеціальності 7.100106 “Виробництво, технічне обслуговування та ремонт повітряних суден і авіадвигунів”.

Laboratory work 1 determination of reynolds’ critical number Brief theoretical information

There are two different liquid flows (and also gases): laminar and turbulent.

Laminar flow is a laminated flow without mixing of liquid particles and with no speed pulsation. In such case all current lines are directed along pipe axis and as a result, there is no mixing of liquid while it is flowing.

Turbulent flow is a flow accompanied by intensive liquid mixing and as well as speeds and pressures pulsation. In turbulent flow, alongside with the main longitudinal liquid flow, svirls, eddies, and cross - motion along the watercourse are set up. Trajectories of separate particles represent complicated curves.

Speed distribution in the cross-section in turbulent flow essentially differs from speed distribution in laminar flow. The speed profiles in laminar and turbulent flows are given in Fig. 1.1. Speed distribution in turbulent flow is more even and speed increasing near the wall is sharper than in laminar flow, which is characterised by parabolic speed profile.

Fig.1.1. Speed Profiles in laminar and turbulent flow

The speed at which the transition from laminar to turbulent flow in a pipe occurs is referred to as critical. The critical speed value depends on liquid viscosity and diameter of the pipe.

With Reynolds’ experiments it was proved that critical speed value varies directly as coefficient of kinematic viscosity and is inversely proportional to the piping diameter .

The dimensionless coefficient of proportionality k in this formula is universal. It is identical for all liquids and gases, and also for any piping diameter. So, as well as transition takes place the parameters characterising flow geometry , kinematics V_cr and its dynamics (relation of forces of viscous resistance and liquid inertia) are represented by the following formula, which is called Reynolds’ critical number:

where is liquid density; isdynamic viscosity coefficient.

Scientific experiments done show us, that laminar flow renewal after its transition to turbulent occurs at minor value of Reynolds’ number than laminar flow disturbance and its transition to turbulent one. So, the Reynolds’ number for turbulent - laminar flow transition is called Low critical, and Reynolds’ number for laminar – turbulent flow transition is called High critical.

Any of two liquid flows can be observed between Low and High Reynolds’ critical numbers. The High critical Reynolds’ number depends on the degree of initial flow turbulence and also on tube gateway conditions, and its value can be different up to 4000. High critical Re number represents only theoretical interest because of instability of observed laminar flow, and more important is Low critical number.

Based on experiments the Low critical number for round conduits stands for 2300.

However, it is not only critical number that characterises the flow change but also actual Reynolds’ number stated by its actual speed is of greatest importance for the development of the science of hydraulics and its industrial application:

(1.1)

So, we have received a criterion for liquid flow shape. With minor values of Reynolds number Re <Re_cr the flow is steady laminar, with major Re >Re_cr - unsteady laminar flow or steady turbulent.

Laminar flow occurs if viscous fluid flows in a pipe, for example, lubricates, glycerine mixtures, etc.

Turbulent flow occurs in plumbing and also in pipes with petrol, kerosene, spirits, acids and other viscous fluids of low kinematic viscosity. Both laminar and turbulent flows occur in aircraft pipes: usually laminar flow occurs in aircraft oil and hydraulic systems and turbulent flow – in fuel and anti-icing systems.

With Reynolds criterion the flow can be determined not only on qualitative, but also on quantitative side, which is significant for determination of energy losses of fluids flowing in pipes.

Reynolds’ apparatus for fluid flow observation and determination of proper Reynolds’ number is usually being used. The principal scheme of the measuring system is shown in Fig. 1.2.

Fig.1.2. Principal scheme of the system for demonstration the kinds of liquid flow and determination of Reynolds’ numbers

Reservoir 1 is filled with water. A glass pipe 4 with faucet 5 for controling the liquid flow rate which is flowing into calibrated tank 6 is fitted to the reservoir. Coloured liquid from tank 2 comes into glass pipe 4 through thin pipe 3 for the kind of liquid flow in the pipe to be observed. If the coloured liquid flows in the pipe without interfusion with original liquid, this is testified as laminar flow. With increasing of speed the coloured liquid is washed out and is mixed with original liquid that indicates a turbulent kind of liquid flow.

The results of experiments are processed by formula (1.1). Water temperature is measured with thermometer which is installed in reservoir 1, and then (see Appendix 1) the coefficient of kinematic viscosity is determined ( =(t)). The pipe liquid speed is determined as average speed V_av of the flow rate Q through cross-section :

Fluid rate is determined by formula:

where W is measured liquid volume, T is time of the calibrating tank having been filled.