The Reynolds number of a flow is the ratio of

Options

A. Gravity to viscous force
B. Gravity force to pressure force
C. Inertial forces to viscous force
D. Viscous forces to pressure forces

Answer

To solve the question regarding the Reynolds number (Re) and its interpretation in terms of forces, we can follow these steps:

### Step 1: Understand the Definition of Reynolds Number
The Reynolds number is defined as:
\[ Re = \frac{\rho v d}{\eta} \]
where:
- \(\rho\) = density of the fluid
- \(v\) = velocity of the fluid
- \(d\) = characteristic length (diameter of the pipe)
- \(\eta\) = dynamic viscosity of the fluid

### Step 2: Identify the Forces Involved
In fluid mechanics, we can relate the Reynolds number to different types of forces:
- **Inertial Force**: This is related to the momentum of the fluid and can be expressed as \(F_i = \rho v^2 A\), where \(A\) is the cross-sectional area.
- **Viscous Force**: This is related to the internal friction of the fluid and can be expressed as \(F_v = \eta \frac{A v}{d}\), where \(d\) is the characteristic length.

### Step 3: Express the Reynolds Number in Terms of Forces
We can rewrite the Reynolds number in terms of the ratio of inertial force to viscous force:
\[ Re = \frac{F_i}{F_v} \]
Substituting the expressions for the forces:
\[ Re = \frac{\rho v^2 A}{\eta \frac{A v}{d}} = \frac{\rho v^2 d}{\eta} \]
This shows that the Reynolds number can be interpreted as the ratio of inertial forces to viscous forces.

### Step 4: Conclusion
From the analysis, we conclude that the Reynolds number is a dimensionless quantity that represents the ratio of inertial forces to viscous forces in a fluid flow.

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

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