The Reynolds number of a flow is the ratio of

Options

A. Viscous force and gravitational force
B. Inertial force and viscous force
C. Inertial force and gravitational force
D. Viscous force and surface energy

Answer

To solve the question regarding the Reynolds number of a flow, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Definition**: The Reynolds number (Re) is a dimensionless quantity that helps predict flow patterns in different fluid flow situations. It is defined as the ratio of inertial forces to viscous forces.

2. **Writing the Expression**: The formula for the Reynolds number is given by:
\[ Re = \frac{\rho V d}{\eta} \]
where:
- \(\rho\) = density of the fluid,
- \(V\) = velocity of the fluid,
- \(d\) = characteristic length (such as diameter of the pipe),
- \(\eta\) = dynamic viscosity of the fluid.

3. **Manipulating the Expression**: To further understand the components of the Reynolds number, we can manipulate the expression:
- Multiply the numerator and denominator by the area \(A\) and velocity \(V\):
\[ Re = \frac{\rho V d}{\eta} \cdot \frac{A V}{A V} = \frac{\rho V^2 A d}{\eta A V} \]

4. **Identifying Forces**: In this expression:
- The term \(\rho V^2 A d\) represents the inertial force (due to the motion of the fluid).
- The term \(\eta A V\) represents the viscous force (due to the fluid's viscosity).

5. **Conclusion**: From the above analysis, we can conclude that the Reynolds number is the ratio of inertial force to viscous force:
\[ Re = \frac{\text{Inertial Force}}{\text{Viscous Force}} \]

6. **Checking Options**: If we check the options provided in the question, we find that option B states that the Reynolds number is the ratio of inertial force to viscous force, which is correct.

### Final Answer:
The Reynolds number of a flow is the ratio of inertial force to viscous force.

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