An oil having kinematic viscosity 1.5 × 10-4 m2/s is flowing through a pipe of 30 mm diameter. For the velocity of oil flow 25 m/s, the Reynold's number is
5000
Reynolds Number Calculation for Oil Flow
The Reynolds number is a dimensionless quantity in fluid mechanics used to predict flow patterns in different fluid flow situations. It helps determine whether the flow is laminar (smooth), turbulent (chaotic), or transitional. It is particularly important when a fluid is flowing through a pipe.
Understanding Key Parameters
To calculate the Reynolds number, we need a few specific fluid and flow properties. Let's break down what each term represents:
- Kinematic Viscosity (\(\nu\)): This measures a fluid's resistance to flow under the influence of gravity. It is the ratio of dynamic viscosity to density. Its unit is typically square meters per second (\(m^2/s\)).
- Pipe Diameter (D): This is the internal diameter of the pipe through which the fluid is flowing. It is usually measured in meters (m).
- Flow Velocity (V): This is the average speed at which the fluid is moving through the pipe. It is typically measured in meters per second (m/s).
Given Data for Oil Flow
Let's list the values provided in the question for the oil flowing through the pipe:
| Parameter | Symbol | Value |
|---|---|---|
| Kinematic Viscosity of oil | \(\nu\) | \(1.5 \times 10^{-4} \text{ m}^2/\text{s}\) |
| Diameter of the pipe | D | \(30 \text{ mm}\) |
| Velocity of oil flow | V | \(25 \text{ m/s}\) |
Before proceeding with the calculation, we must ensure all units are consistent. The pipe diameter is given in millimeters (mm), so we need to convert it to meters (m):
Pipe Diameter (D) = \(30 \text{ mm} = 30 \times 10^{-3} \text{ m} = 0.03 \text{ m}\)
Calculating the Reynolds Number
The formula for the Reynolds number (\(Re\)) for internal flow (like flow through a pipe) is given by:
\(Re = \frac{VD}{\nu}\)
Where:
- \(V\) = Velocity of the fluid flow
- \(D\) = Diameter of the pipe
- \(\nu\) = Kinematic viscosity of the fluid
Now, let's substitute the given values into the formula:
\(Re = \frac{(25 \text{ m/s}) \times (0.03 \text{ m})}{1.5 \times 10^{-4} \text{ m}^2/\text{s}}\)
\(Re = \frac{0.75 \text{ m}^2/\text{s}}{1.5 \times 10^{-4} \text{ m}^2/\text{s}}\)
\(Re = \frac{0.75}{0.00015}\)
\(Re = 5000\)
Result and Conclusion
The calculated Reynolds number for the given oil flow conditions is \(5000\). This value typically indicates that the flow is in the transitional or turbulent regime for pipe flow, as the critical Reynolds number for internal flow is generally around 2000 to 2300.
Important Questions from Dimensionless Number
Euler's dimensionless number relates the following:
- In fluid flow diagrams that plot the friction factor against the Reynolds number, such as the Moody chart, what crucial additional parameter is commonly represented by a series of curves?
When Mach number is less than unity, the flow is called-
The square root of the ratio of the inertia force due to flow to the elastic force of fluid is known as-
Euler number is related to
