Fluid Mechanics Lab Reynolds Experiments

The information in this document has been extracted from User Manual for Reynolds Number and Transitional Flow manufactured by TecQuipment Ltd

AIM The aim of this experiment is to investigate different flow regimes in pipes and find critical Reynolds number.

DESCRIPTION OF THE APPARATUS Figure 1 shows the Reynolds Number measurement apparatus. The basic apparatus consists of a precision bore glass tube of 12 mm internal diameter which is supported in a large shroud of rust-proof material. The shroud is open at the front and the inside surface is a light colour to assist flow visualisation. At the top of the shroud is a constant head tank from which water can pass into the tube via a specially shaped bell-mouth entry. Water is supplied to the tank via a diffuser located below the bell-mouth. This provides a nearly uniform supply of water to all sides of the bell-mouth. Further smoothing of the flow is achieved by passing the water through a stilling bed consisting of glass beads packed above the diffuser. In this way steady uniform flow conditions are obtained at entry to the bell-mouth.

Figure 1- Sketch of Reynolds apparatus

The supply pipe to the tank is at the rear of the apparatus and can connect either directly to a tap or to the outlet of the temperature control module. A fixed overflow pipe is also fitted to the tank to ensure a constant head of water. Connect this pipe to a drain using a length of flexible hose supplied.

A valve at the outlet from the tube controls the flow through the glass tube. The outlet should be connected via a loose hose to convenient drain. Flow is measured by timing the collection of a known

quantity of water in a suitable measuring vessel or by a flowmeter has been connected to drain pipe. It is suggested to measure the flow rate using both methods.

The behaviour of the flow in the tube can be observed by injecting a fine filament of dye into the tube using the special dye injector provided. This consists of a fine injector tube connected via a valve to a dye reservoir. The assembly mounts onto a plate, which fits on the top of the constant head tank. The injector tube is positioned such that its outlet is in the centre of the bell-mouth entry.

The complete apparatus is supported on a triangular base with adjustable feet.

THEORY

What, then, determines whether the flow will be laminar or turbulent in a given situation? We have seen that laminar flow is the result of viscous forces and that turbulent flow is in some way related to inertia forces. This was realised by Reynolds who postulated that the nature of flow depended on the ratio of inertia to viscous forces. This led to the derivation of a nondimensional variable, now called Reynolds number Re - which expresses this ratio.

On physical grounds we may say that the inertia forces are proportional to mass multiplied by velocity change divided by time, Since mass divided by time is the mass flow rate and this is equal to density multiplied by cross sectional area multiplied by velocity u we may write:

Inertia forces d2u.u , where d is the diameter of the pipe.

Similarly the viscous forces are given by shear stress multiplied by area so, using

= du/dy

we may write:

viscous forces ud d2

Dividing the inertia forces by the viscous forces we obtain Reynolds number as:

= 22

=

The term / is called the kinematic viscosity, , and it is often convenient to write the above equation as:

=

The important discovery made by Reynolds was that for normal flow in a pipe, the transition between laminar and turbulent flow always occurs at approximately the same value of Re, irrespective of the fluid and the size of the pipe. This, therefore, enables prediction of flow conditions in pipes of any size carrying the fluid. It must be appreciated, however, that there is never a precise point at which transition between laminar and turbulent flow occurs.

Consider the case of increasing velocity in a pipe, initially the viscous forces dominate and the flow is laminar. As velocity increases occasional eddies form but these are quite quickly damped out by viscous effects. Further increase in velocity is accompanied by an increase in the number of eddies

until a point is reached where the complete flow is subject to turbulent mixing and can be considered fully turbulent. Transition from fully laminar to fully turbulent flow may occur interspersed with periods of quite steady laminar flow. The final transition to fully turbulent flow tends to be more well-defined since above a certain level of turbulence becomes self-generating and a few disturbances will set the whole flow into turbulent motion.

Now consider the case of reducing velocity. In this case the turbulent motions tend to continue until the velocity is below that at which turbulent flow originally started. Eventually, however, a point is reached when the viscous forces damp out the eddies and the flow reverts quite quickly to laminar. This behaviour can be demonstrated by flow visualisation and also by measuring head losses along pipes.

PROCEDUER OF EXPERIMENT AND RESULTS The basic procedure which can be used for all tests, demonstrates how the conditions in the pipe vary with flow velocity and that the changes occur over a range of velocity (and therefore of Reynolds number). The Reynolds number can be calculated for each condition from the pipe diameter, velocity and the viscosity of water for the particular temperature of test. Sample calculations are given later in this section . The basic procedure is as follows:

1. Set up the apparatus as previously described, turn on the water supply, and partially open the discharge valve at the base of the apparatus.

2. Adjust the water supply until the level in the constant head tank is just above the overflow pipe and is maintained at this level by a small flow down the overflow pipe. This is the condition required for all tests and at different flow rates through the tube; the supply will need to be adjusted to maintain it. At any given condition the overflow should only be just sufficient to maintain a constant head in the tank.

3. Open and adjust the dye injector valve to obtain a fine filament of dye in the flow down the glass tube. If the dye is dispersed in the tube reduced the water flow rate by closing the discharge valve and adjusting the supply as necessary to maintain the constant head. A laminar flow condition should be achieved in which the filament of dye passes down the complete length of the tube without disturbance.

4. Slowly increase the flow rate by opening the discharge valve until disturbances of the dye filament are noted (see Figure 2b). This can be regarded as the starting point of transition to turbulent flow. Increase the water supply as required to maintain constant head conditions.

5. Record the temperature of the water using the thermometer, then measure the flow rate by timing the collection of a known quantity of water from the discharge pipe or by flowmeter if available.

6. Further increase the flow rate as described above until the disturbances increase such that the dye filament becomes rapidly diffused as shown in Figure 2c. Small eddies will be noted just above the point where the dye filament completely breaks down. This can be regarded as the onset of fully turbulent flow. Record the temperature and flow rate as in step (5).

7. Now decrease the flow rate slowly until the dye just returns to a steady filament representing laminar flow and again record the temperature and flow rate.

8. For each flow rate fill in data in the table below.

Volume

Time

Flow rate from flowmeter

Temperature

Pipe diameter

Velocity in the pipe

Viscosity

Re

Type of flow

(L) (S) (L/s) (oC) (mm) (m/s) (m2/s) 10-6 (Vd/) The following figure shows the flow pattern for laminar, transitional and turbulent flow.

Figure 2- Flow pattern for laminar, transitional and turbulent flow

Report: Your report should be typed and include the following:

Introduction, Aim of the experiments, Entre data in the table and estimate Reynolds number, Plot change of velocity with Re. Estimate critical Reynolds number, Conclusions

Re