Which one of the following statements regarding a completely enclosed fluid is true?

Options

A. Any change in the applied pressure of the fluid produces a change in pressure that depends on direction.
B. The pressure at all points within the fluid is independent of any pressure applied to it.
C. Any change in applied pressure produces an equal change in pressure at all points within the fluid.
D. An increase in pressure in one part of the fluid results in an equal decrease in pressure in another part.

Answer

To determine which statement regarding a completely enclosed fluid is true, we can analyze each option based on the principles of fluid mechanics, particularly Pascal's Law.

### Step-by-Step Solution:

1. **Understanding Pascal's Law**:
- Pascal's Law states that when pressure is applied to a confined fluid, the pressure change is transmitted undiminished throughout the fluid in all directions. This means that any change in pressure at one point in the fluid will be felt equally at all other points.

2. **Analyzing Option A**:
- **Statement**: "Any change in the applied pressure of the fluid produces a change in pressure that depends on direction."
- **Evaluation**: This statement is false. According to Pascal's Law, pressure changes do not depend on direction; they are transmitted equally in all directions.

3. **Analyzing Option B**:
- **Statement**: "The pressure at all points within the fluid is independent of any pressure applied to it."
- **Evaluation**: This statement is also false. The pressure at points within the fluid is dependent on the applied pressure. If pressure is applied at one point, it affects the pressure throughout the fluid.

4. **Analyzing Option C**:
- **Statement**: "Any change in applied pressure produces an equal change in pressure at all points in the fluid."
- **Evaluation**: This statement is true. According to Pascal's Law, any change in pressure at one point in a confined fluid results in an equal change in pressure at all other points.

5. **Analyzing Option D**:
- **Statement**: "An increase in pressure at one part of the fluid results in a decrease in another part."
- **Evaluation**: This statement is false. An increase in pressure at one point in the fluid results in an increase in pressure throughout the fluid, not a decrease.

6. **Conclusion**:
- After evaluating all options, the correct answer is **C**: "Any change in applied pressure produces an equal change in pressure at all points in the fluid."