Pressure gradient in the horizontal direction in a static fluid is represented by (z-direction is vertically upwards, and x-axis is along horizontal, d is density of fluid):

Options

A. `(delp)/(delz)=-dg`
B. `(delp)/(delx)=dg`
C. `(delp)/(delx)=0`
D. `(delp)/(delz)=0`

Explanation

To solve the problem of finding the pressure gradient in the horizontal direction in a static fluid, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Static Fluid**:
- A static fluid is one that is not in motion. This means that there are no velocity gradients within the fluid, and the fluid is at rest.

2. **Identify the Direction of Interest**:
- The question specifically asks about the pressure gradient in the horizontal direction. We will denote the horizontal direction as the x-axis.

3. **Apply Pascal's Law**:
- According to Pascal's law, in a static fluid, pressure at any point is the same in all directions. Therefore, if we consider any two points in the horizontal direction (along the x-axis), the pressure at these two points will be equal.

4. **Define Pressure Gradient**:
- The pressure gradient in the x-direction is defined mathematically as the derivative of pressure with respect to x, denoted as \( \frac{\partial P}{\partial x} \).

5. **Evaluate the Pressure Gradient**:
- Since the pressure is constant throughout the fluid in the horizontal direction (due to the fluid being static), the change in pressure with respect to x is zero. Thus, we have:
\[ \frac{\partial P}{\partial x} = 0 \]

6. **Conclusion**:
- Therefore, the pressure gradient in the horizontal direction in a static fluid is represented by:
\[ \frac{\partial P}{\partial x} = 0 \]
- This indicates that there is no change in pressure along the horizontal direction.

### Final Answer:
The pressure gradient in the horizontal direction in a static fluid is represented by \( \frac{\partial P}{\partial x} = 0 \).