Reynolds Experiment

REYNOLDS EXPERIMENT OBJECTIVE: To perform the Reynolds experiment for determination of different regimes of flow.

APPARATUS: 1. 2. 3. 4. 5.

A consta constant nt head head tank filled filled with with water water A small tank containing containing dye (sp. (sp. weight of dye same as that of water) A horizon horizontal tal glass glass tube tube provided provided with with a bell bell mouthed mouthed entran entrance ce A regu regula lati ting ng valv valvee A stop top watch

THEORY: The flow of real fluids can basically 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 Reynolds conducte conducted d an experim experiment ent for observ observatio ation n and det determ erminat ination ion of these 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 dye filam filamen entt appe appear ared ed as strai straight ght line line throu through gh the length length of the tube and 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 = ρVD/ µ = VD/v ; v = μ/ρ Where: Re = Reynolds number V = Velocity of flow D = characteristic length=diameter in case of pipe flow ρ = 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 or viscous while offer Re>4000 it is turbulent flow and for 2000
PROCEDURE: 1. Fill the water tank with water and allow it to stand for some time so that the water comes to rest. 2. Note the temperature of water. 3. To maintain constant head in the tank by adjusting inlet valve and regulating valve. 4. Partially open the outlet valve of the glass tube and allow the flow to take place at a very low rate. 5. 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. 6. Measure the discharge by collecting water in the measuring tank for a certain interval of time. 7. Repeat the steps 3 and 5 for different discharges. 8. Again note the temperature of water.

OBSERVATIONS: Mean temperature of water – T = Kinematic viscosity of water- v = Diameter of glass tube- D =

Temperature -T(oC)

• •

Dynamic Viscosity Kinematic Viscosity -µ-ν(N s/m2) x 10-3 (m2/s) x 10-6

0

1.787

1.787

5

1.519

1.519

10

1.307

1.307

20

1.002

1.004

30

0.798

0.801

40

0.653

0.658

50

0.547

0.553

60

0.467

0.475

70

0.404

0.413

80

0.355

0.365

90

0.315

0.326

100

0.282

0.294

1 N s/m2 = 1 Pa s = 10 poise = 1,000 milliPa s 1 m2/s = 1 x 104 cm2/s =1 x 104 stokes = 1 x 106 centistokes

CALCULATIONS: Perform the following calculations for each set of readings: Discharge –Q = Axh /t Velocity of flow – V = 4Q / (πD2) ; Q = AV Reynolds number –Re = VD/v

RESULT: