Reynolds Number and Flow Regimes in Pipes
(A) Less than 2000
(B) Between 2000 and 2800
(C) More than 2800
(D) None of the above
Explanation
The nature of flow in a pipe is determined by the Reynolds number (Re), which indicates whether the flow is laminar, transitional, or turbulent. The flow regimes are defined as follows:
- Laminar Flow: Re < 2000 (smooth, orderly flow)
- Transitional Flow: 2000 < Re < 4000 (unstable, fluctuating between laminar and turbulent)
- Turbulent Flow: Re > 4000 (chaotic, irregular flow)
In the transitional range (2000 < Re < 4000), the flow is neither purely laminar nor turbulent, making it unpredictable and sensitive to disturbances.
Reynolds Number in Pipe Flow and Open Channel Flow
The Reynolds number is calculated differently for pipe flow and open channel flow, reflecting their distinct characteristics. Below is a comparison of the two:
1. Basic Definition
| Aspect | Pipe Flow | Open Channel Flow |
|---|---|---|
| Medium | Fully enclosed flow (pressurized) | Flow with a free surface open to atmosphere (e.g., rivers) |
| Reynolds Number | Re = ρ V Dμ | Re = ρ V Rμ, where R = AP (Hydraulic Radius) |
Where: ρ = fluid density, V = velocity, D = pipe diameter, μ = dynamic viscosity, A = flow area, P = wetted perimeter.
2. Critical Reynolds Number & Flow Regimes
| Flow Regime | Pipe Flow (Based on Diameter, D) | Open Channel Flow (Based on Hydraulic Radius, R) |
|---|---|---|
| Laminar Flow | Re < 2000 | Re < 500 |
| Transitional Flow | 2000 < Re < 4000 | 500 < Re < 2000 |
| Turbulent Flow | Re > 4000 | Re > 2000 |
3. Applications & Behavior
| Aspect | Pipe Flow | Open Channel Flow |
|---|---|---|
| Examples | Water supply, oil pipelines, gas flow | Rivers, canals, sewers, irrigation channels |
| Driving Force | Pressure difference | Gravity |
| Surface | No free surface | Has a free surface |
| Effect of Roughness | Affects turbulent regime more | Affects even laminar flow due to shallow depths |
4. Hydraulic Radius in Open Channel Flow
In open channel flow, the hydraulic radius (R) is used instead of diameter:
R = AP
Where: A = cross-sectional area of flow, P = wetted perimeter.
Summary Table
| Flow Type | Reynolds Number Formula | Laminar Limit | Turbulent Start |
|---|---|---|---|
| Pipe Flow | ρ V Dμ | Re < 2000 | Re > 4000 |
| Open Channel Flow | ρ V Rμ | Re < 500 | Re > 2000 |
Key Notes
- The Reynolds number is a dimensionless quantity that predicts the flow regime based on fluid properties and geometry.
- Transitional flow is unstable and sensitive to factors like pipe roughness or external disturbances.
- In open channel flow, the hydraulic radius accounts for the free surface and irregular channel shapes.
- Understanding flow regimes is critical for designing efficient pipelines, channels, and hydraulic systems.
Note: Accurate determination of the Reynolds number ensures proper design and operation of fluid flow systems in civil, mechanical, and hydraulic engineering.
More solved questions of APSC WRD AE 2019, HERE
For APSC Water Resources Civil 2019 Question Paper, Click Here
For APSC Previous Year AE Question Paper, Click Here
For APSC Previous Year JE Question Paper, Click Here