To perform the Reynolds experiment for determination of different regimes of flow.
The flow of real fluids can basically occur under two very different regimes namely laminar and turbulent flow. The laminar flow is characterized by fluid particles moving in the form of lamina sliding over each other, such that at any instant the velocity at all the points in particular lamina is the same. The lamina near the flow boundary move at a slower rate as compared to those near the center of the flow passage. This type of flow occurs in viscous fluids , fluids moving at slow velocity and fluids flowing through narrow passages.
The turbulent flow is characterized by constant agitation and intermixing of fluid particles such that their velocity changes from point to point and even at the same point from time to time. This type of flow occurs in low density
Fluids, flow through wide passage and in high velocity flows.
Reynolds conducted an experiment for observation and determination of these regimes of flow. By introducing a fine filament of dye in to the flow of water through the glass tube ,at its entrance he studied the different types of flow. At low velocities the dye filament appeared as straight line through the length of the tube and parallel to its axis, characterizing laminar flow. As the velocity is increased the dye filament becomes wavy throughout indicating transition flow. On further increasing the velocity the filament breaks up and diffuses completely in the water in the glass tube indicating the turbulent flow.
After conducting his experiment with pipes different diameters and with water at different temperatures Reynolds concluded that the various parameters on which the regimes of flow depend can be grouped together in a single non dimensional parameter called Reynolds number. Reynolds number is defined as, the ratio of inertia force per unit volume and is given by
Re=vD?/ µ =VD/v
V -velocity of flow
D-characteristic length=diameter in case of pipe flow
?-mass density of fluid
µ-dynamic viscosity of fluid
v -kinematic viscosity of fluid
Reynolds observed that in case of flow through pipe for values of Re<2000 the flow is laminar while offer Re>40000 it is turbulent and for 2000<Re<4000 it is transition flow.
A stop watch, a graduated cylinder ,and Reynolds apparatus which consists of water tank having a glass tube leading out of it. The glass tube has a bell mouth at entrance and a regulating valve at outlet ,a dye container with an arrangement for injecting a fine filament of dye at the entrance of the glass tube.
i. Fill the water tank with water and allow it to stand for some time so that the water comes to rest.
ii. Note the temperature of water.
iii. Partially open the outlet valve of the glass tube and allow the flow to take place at a very low rate.
iv. Allow the flow to stabilize then open the valves at the inlet of the dye injector and allow the dye to move through the tube.Observe the nature of the filament.
v. Measure the discharge by collecting water in the graduated cylinder for a certain interval of time.
vi. Repeat the steps 3 and 5 for different discharges
vii. Again note the temperature of water
Mean temperature of water – t -
Kinematic viscosity of water-v-
Diameter of glass tube-D-
Perform the following calculations for each set of readings
Discharge -Q-Axh /t
Velocity of flow – V-4Q /(?D2)
Reynolds number -Re-VD/v