When a liquid flows in a tube, there is relative motion between adjacent layers of the liquid. This force is called the viscous force which tends to oppose the relative motion between the layers of the liquid. Newton was the first person to study the factors that govern the viscous force in a liquid. According to Newton’s law of viscous flow, the magnitude of the viscous force on a certain layer of a liquid is given by
` F = - eta A (dv)/(dx)`
where A is the area of the layer ` (dv)/(dx) ` is the velocity gradient at the layer and ` eta ` is the coefficient of viscosity of the liquid.
If f is the frictional force between a solid sliding over another solid, and F is the viscous force when a liquid layer slides over another, then :

Options

A. f is independent of the area of the solid sliding over another solid.
B. f depends on the relative velocity of one solid with respect to the other
C. F depends on the area of the layer of the liquid.
D. F is independent of the relative velocity between adjacent layers.

Explanation

To solve the question regarding the relationship between viscous force in liquids and frictional force in solids, we will analyze the statements provided and apply Newton’s law of viscous flow.

### Step-by-Step Solution:

1. **Understanding Viscous Force**:
- According to Newton's law of viscous flow, the viscous force \( F \) acting on a layer of liquid is given by:
\[ F = -\eta A \frac{dv}{dx} \]
- Here, \( \eta \) is the coefficient of viscosity, \( A \) is the area of the layer, and \( \frac{dv}{dx} \) is the velocity gradient.

2. **Understanding Frictional Force**:
- The frictional force \( f \) between two solid surfaces is generally given by:
\[ f = \mu N \]
- Where \( \mu \) is the coefficient of friction and \( N \) is the normal force. Importantly, this force does not depend on the area of contact.

3. **Analyzing the Options**:
- **Option A**: "Small \( f \) is independent of the area of the solid sliding over another solid."
- This is **correct** because the frictional force for solids does not depend on the area of contact.

- **Option B**: "Small \( f \) depends on the relative velocity of one solid with respect to the other."
- This is **incorrect** because the frictional force is independent of the relative velocity between the two solids.

- **Option C**: "F depends on the area of the layer of the fluid."
- This is **correct** since the viscous force \( F \) is directly proportional to the area \( A \) as seen in the formula \( F = -\eta A \frac{dv}{dx} \).

- **Option D**: "F is independent of relative velocity between the adjacent layers."
- This is **incorrect** because the viscous force does depend on the velocity gradient \( \frac{dv}{dx} \).

4. **Conclusion**:
- The correct options are A and C. The frictional force \( f \) is independent of area, while the viscous force \( F \) is dependent on the area of the fluid layer.