The ratio of inertial force to viscous force represets

Options

A. Magnus effect
B. Reynolds number
C. Torricell's law
D. Relative density

Explanation

To solve the question regarding the ratio of inertial force to viscous force, let's break it down step by step:

### Step 1: Understand the Forces
In fluid mechanics, two important forces are considered when analyzing fluid flow:
- **Inertial Force (F_inertial)**: This force is associated with the mass of the fluid and its acceleration. It can be represented as \( F_{inertial} = \rho v^2 L \), where \( \rho \) is the fluid density, \( v \) is the velocity of the fluid, and \( L \) is a characteristic length.
- **Viscous Force (F_viscous)**: This force arises due to the viscosity of the fluid, which is a measure of its resistance to flow. It can be represented as \( F_{viscous} = \mu \frac{v}{L} A \), where \( \mu \) is the dynamic viscosity, \( v \) is the velocity, \( L \) is the characteristic length, and \( A \) is the area.

### Step 2: Write the Ratio
The ratio of inertial force to viscous force is given by:
\[ \text{Ratio} = \frac{F_{inertial}}{F_{viscous}} \]

### Step 3: Substitute the Expressions
Substituting the expressions for the inertial and viscous forces, we get:
\[ \text{Ratio} = \frac{\rho v^2 L}{\mu \frac{v}{L} A} \]

### Step 4: Simplify the Ratio
This can be simplified further. Assuming \( A = L^2 \) (for a characteristic area in a flow), we can rewrite the ratio as:
\[ \text{Ratio} = \frac{\rho v^2 L}{\mu \frac{v}{L} L^2} = \frac{\rho v^2 L^2}{\mu v} = \frac{\rho v L}{\mu} \]

### Step 5: Identify the Result
This ratio is known as the **Reynolds number (Re)**:
\[ Re = \frac{\rho v L}{\mu} \]

### Conclusion
Thus, the ratio of inertial force to viscous force represents the **Reynolds number**.