Reynolds_experiment雷诺实验(英文版)

Reynolds experiment

Aim of the experiment

1.Observe the laminar and turbulent flow, and the process of transition from one state to the

other.

2.Measure the critical Reynolds number and develop the skills on how to distinguish the

pipe flow state.

3.Study the dimensional analysis method to analyze the experiment, confirming the

criterion number of flow state for a non-circular pipe.

Experimental apparatus

1. The figure of the apparatus

Figure 1 shows the experimental apparatus and the name of each part.

Figure 1. 1: Self-circulating water supply, 2: Hydraulic bench, 3: Speed controller, 4: Constant head water tank, 5: Coloured water pipe, 6: Perforated plate, 7: Overflow, 8: Experiment pipe, 9:

Flow rate control valve

2. The illustration of installation and the method of operation.

The water flow rate is controlled by a speed controller 3, making constant pressure water tank 4 keep the state which micro overflow in order to improve the stability of water flow. There are many clapboards to keep water stability in this experimental device, shorten the time spend on stabilize the water to 3-5 min. Colure water flow into pipe 8 through colure water pipe 5, we can distinguish the flow state according to whether the colure water disperse. In order to avoid pollution of water due to the self-circulation, we use the special colure water. The flow rate in the experiment is controlled by valve 9.

Theory.

In 1883, Osborne Reynolds using the experimental device which is similar with the device shown in Figure 4.2.1, observed the laminar state and turbulent state in fluid flow: The colored filament is straight and smooth for low speeds, this state is laminar flow. However, the colored filament breaks off and disperses almost uniformly for high velocities, and this state is turbulent flow. Reynolds also found that there is a critical velocity v c from laminar to turbulent state. v c depends on the viscosity of the fluid ν and the diameter of pipe d. The value of v c should be known in different situations when we want to know the flow state. The contribution of Reynolds is not only to find the two flow states, but also used dimensional analysis to analyze the experiment and get the Reynolds number which simplifies the problem. The following is dimensional analysis.

Since: v ୡ=f(ν,d)

According to the dimensional analysis method:

v ୡ=k ୡν஑భd ஑మ

ሾLT ିଵሿ=ሾL ଶT ିଵሿ஑భሾLሿ஑మ

αଵ=1,αଶ= −1

v ୡ= k ୡ஝ୢ or k ୡ= ୴ౙୢ஝

Reynolds concluded the measurement of the critical value from laminar flow to turbulent flow

state in pipe flow, validating k ୡ is constant. So, ୴ୢ஝ can be used to distinguish between the flow

state in any situation. Because of Reynolds contribution, ୴ୢ஝ is called the Re number. So, there is

Re = vd ν= 4q ୚πνd =Kq ୴ V: velocity of flow

ν: kinematic viscosity of flow

d: diameter of tube

q ୚:flow rate in pipe K: calculation constant, K = ସ஠஝ୢ. There is a lower critical Re number when flow transits from turbulent to laminar state. There is an upper critical Re c ’ number when flow transits from laminar to turbulent state. The value of upper critical Re c number is not stable because of external disturbances. However, the value of lower critical number is stable. Hence, generally the lower critical Re c number is used to distinguish between the flow regimes. The value of Re c number is 2300 according to the