Report Renoylds Number

TITTLE: Reynolds Number OBJECTIVES: 1. To investigate the dependence of flow pattern on Reynolds number. 2. To investigate the nature of the flow in a pipe by observing the behavior of a filament of dye injected into the fluid. 3. To demonstrate the change, or ‘transition’, between laminar and turbulent flow by varying the flow rate. THEORY: Consider the case of a fluid moving along a fixed surface such as the wall of a pipe. A shear stress given by: τ=μdudy The nature of flow depends on the ratio of inertia to viscous forces. Inertia force of the fluid particles is the force that tends to carry each fluid particle to move at its own accelerated direction. While viscous force due to the surrounding fluid will tend to make the individual fluid particle conform to the motion of the rest of the stream. For flow in a circular pipe, Inertia force ∝ρd²u.u Where d is the diameter of the pipe. Similarly the viscous forces are given by shear stress multiplied by area so, using equation (10, we may write: Viscous force ∝μudd² Dividing the inertia force by the viscous force we obtain a non-dimensional variable, namely Reynolds number, Re: Re=ρd²u²μud=ρduμ The term μ/ρ is called the kinematic viscosity, v and it is often convenient to write Re=udv

APPARATUS:

PROCEDURES: 1. The constant head bank with water to the level of overflow pipe was filling up. 2. The dye injector with the dye was filling up. 3. For laminar flow, the discharge control valve was adjusting in such a way the dye will flow down in a straight line. Make sure the water level at par with the overflow pipe. 4. Once the laminar flow occurred, the time for collection of 200ml water from the drain pipe was starting. 5. Procedure 3 for transition and turbulent flow was repeating with timing for 200ml of water from the drain pipe. 6. Water temperature was recording at any time during the experiment. 7. The whole experiment whole repeating by reversing condition starting with turbulent flow, transition was following by laminar flow.

EXPERIMENTAL DATA:

Table 1: Increasing velocity

Temperature

Condition

(⁰C)

29 29 29

Fully laminar Transition Fully turbulent

Time for

Velocity, u

Kinematic

200ml

(s)

Viscosity, v x

10.31 5.59 1.69

1.098X10 ³̄ 2.025X10 ³̄ 6.697X10 ³̄

Re

(s) 0.8174X10 ⁶̄ 0.8174X10 ⁶̄ 0.8174X10 ⁶̄

201.49 371.6 1228.96

Re

Table 2: Decreasing velocity Temperature

Condition

(⁰C)

29 29 29

Fully turbulent Transition Fully laminar

CALCULATION: 200 ml

liter

Time for

Velocity, u

Kinematic

200ml

(s)

Viscosity, v x

2.34

4.837X10 ̄³

(s) 0.8174X10 ̄⁶

887.63

7.06 12.28

1.603X10 ³̄ 9.217X10 ⁴̄

0.8174X10 ⁶̄ 0.8174X10 ⁶̄

294.16 169.14

1000ml = 1 l 200ml = 0.2l 1l

m³

1l = 1000m³ 0.2l = 0.0002m³

T(⁰C) velocity,μ 25

dynamic 0.891X10 ̄³

29

μ

30

0.798X10 ̄³

Interpolation A = πd24 =π(15X10²4

29 -2530 -25= μ -0.891X10 ̄ ³0.798X10 ̄³ μ=0.8174X10 ̄³

= 0.01767 m² For increasing velocity: u = QA = 0.000210.310.01767 = 1.098X10 ̄³ u = QA

Re = udv =1.098X10 ̄ ³(0.15)0.8174X10 ̄³ = 201.49

= 0.00025.590.01767

Re = udv

= 2.025X10 ̄³

= 2.125X10 ̄ ³(0.15)0.8174X10 ̄³

u = QA = 0.00021.690.01767 = 6.697X10 ̄³

= 371.6 Re = udv = 6.697X10 ̄ ³(0.15)0.8174X10 ̄³ = 1228.96

For decreasing velocity u = QA

= 0.00022.340.01767

Re = udv

= 4.837X10 ̄³

=4.837X10 ̄ ³(0.15)0.8174X10 ̄³

u = QA = 0.00027.060.01767 = 1.63X10 ̄³ u = QA = 0.000212.280.01767 = 9.217X10 ̄⁴

= 887.63 Re = udv = 1.63X10 ̄ ³(0.15)0.8174X10 ̄³ = 296.16 Re = udv = 9.217X10 ̄ ⁴(0.15)0.8174X10 ̄³ = 1228.96

DISCUSSION:

1. Write down your observation in term of valve opening and flow condition The observation that is obtained if the valve opened larger, the velocity will increase and the flow condition will become turbulence. For the small valve opening, the velocity will decrease and the flow will become laminar. The flow between laminar and turbulence is called as transition flow.

2. What is the relationship between velocity and flow condition? Justify your answer in term of viscous force. For higher velocity, the flow will become turbulent and for slower velocity the flow will become laminar. The transition occurs between velocity or turbulence and laminar. For higher velocity, the flow have low internal resistant. This can cause the flow have least viscous force than the water inertia that makes the dye-spread around and dispread in the water.

3. What is happening to the flow condition in procedure? The first observation was there were nothing that can be seen in the test pipe because when the dye are at the test pipe, it will spread to the water and show it was in the turbulent condition. The second observation was dye is in shale linear in the test pipe which shows the laminar flow.

4. Describe in detail on how the Reynolds number affects the flow? The Reynolds number can show how the flow condition when the Reynolds number is less than 2300 that shows that the flow is fully laminar. For Reynolds number 2300 to 4000 the flow are in the transition state and when the Reynolds number shows more than 4000 that shows the flow are at fully turbulent condition.

CONCLUSION:

Each flow of fluid have own characteristic motion whether is smooth and orderly while some rather chaotic. The nature of flow depends on the ratio of inertia to viscous force. The highly disordered fluid motion characterized by smooth layers of fluid is called laminar. The highly disordered fluid motion typically occurs at high velocity and it is characterized by velocity fluctuation are called as turbulent. Transition occurs of increasing of velocity from laminar flow to turbulent flow. All of this correlation within the inertia force and the fluid itself that tends to carry each partial to move at its own path. Viscous force tends to make the individuals fluid particle due to the surrounding.

Fluids follow to the motion of the rest of the flow. In this experiment, for the example increasing velocity, the Reynolds number for laminar is 167.82. Transition flow is 804.10. This is difference from the theoretical valve of Reynolds number that is for fully laminar is less than 2300 and transition is between 23000 and 4000.

QUESTION:

Identify and explain the factors that determine whether the flow will be laminar or turbulent. For practically, from our identification to determine the flow of the dye substances will be laminar or turbulent is the valve. This valve plays the major role in determining whether the flow is to laminar or turbulent. If the valve is opened larger, the velocity of water moving inside the pipe will decrease and flow condition will become turbulent. If the valve opened smaller, the velocity of water moving inside the pipe will decreased and flow become laminar. If the valve opened medium, the flow becomes in between laminar and turbulent that is transition flow. The next factor identified is the velocity of water moving in the pipe. This is because when the velocity is higher, the flow become turbulent and if the velocity is lower, the flows become laminar. The higher the velocity, the lower the internal resistant that also could included in the factors to determine the flow is laminar, transition and turbulent.