Reynolds number and its applications- Fluid mechanics .pptx

Fluid mechanics - Reynolds number
The dimensionless number to describe the flow characteristics of a fluid .

1. Reynolds number

2. What is Reynolds number ? The Reynolds number (Re) is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces.

3. We can conduct a simple experiment by carefully injecting a dye into the liquid flowing in a pipe.
At low flow rates, the dye moves in a straight-line manner in the axial direction, as shown in Figure . As the flow rate increases to some intermediate level, the dye begins to blur at some distance away from the injection point. The blurring of the dye is caused by movement of some of the dye in the radial direction. At high flow rates, the dye becomes blurred immediately upon injection. At these high flow rates, the dye spreads in a random manner along both the radial and axial direction.

4. The straight-line flow observed at low flow rates is called laminar flow ; At intermediate flow rates, the flow is called transitional flow ; And the erratic flow obtained at higher flow rates is called turbulent flow . The flow characteristics for laminar flow are influenced by liquid properties, flow rate, and the dimensions of liquid-solid interfaces. As the mass flow rate is increased, the forces of momentum or inertia increase; but these forces are resisted by friction or viscous forces within the flowing liquid.

5. As these opposing forces reach a certain balance, changes in the flow characteristics occur. Based on experiments conducted by Reynolds (1874),¹ the inertial forces are a function of liquid density, p, tube diameter, D, and average fluid velocity . The viscous forces, on the other hand, are a function of liquid viscosity. A dimensionless number, called a Reynolds number, is defined as the ratio of the inertial to the viscous forces:

6. A Reynolds number is most useful in quantitatively describing the flow characteristics of a fluid flowing either in a pipe or on the surfaces of objects of different shapes. We no longer need to limit ourselves to qualitative descriptions of flow such as low, intermediate, or high. Instead, we can use a Reynolds number to specifically identify how a given liquid would behave under selected flow conditions.

7. The Reynolds number provides an insight into energy dissipation caused by viscous effects. when the viscous forces have a dominant effect on energy dissipation, the Reynolds number is small, or flow is in a laminar region. As long as the Reynolds number is 2100 or less, the flow characteristics are laminar or stream line. A Reynolds number between 2100 and 4000 signifies a transitional flow. A Reynolds number greater than 4000 indicates turbulent flow denoting small influence of viscous forces on energy dissipation.

8. Unit : Unit = kg/m³ × m/s × m ÷ kg/ ms = Kg×m² / m³s × ms / kg = 1 No unit left, so it’s a dimensionless number

9. Applications Mixing and stirring : Design appropriate mixing systems for optimal efficiency ( blending ingredients , dispersing aditives or maintaining uniformity in food processing) Heat exchangers and pasteurization: Optimising heat transfer Pump and piping designs : To assist in designing pumps and pipes to ensure that the flow remain within the designed resin preventing issues such as cavitation and ensuring efficient transport

10. 4. Chocolate manufacturing: For optimising the flow of chocolate within the conching machine. 5. Spray drying and atomization : (liquids are transferred into powders or fine droplets) In controlling the breakup and dispersion of the liquid. This is vital for achieving decide particle size and distribution in products like powdered flavours milk products or instant coffee.

11. Thank you