Two parallel layers of water are moving with a relative velocity of 10 cm/s. What will be the velocity gradient if the perpendicular distance between the layers is 0.2 cm.

Answer

To find the velocity gradient between two parallel layers of water moving with a relative velocity, we can use the formula for velocity gradient, which is defined as:

\[ \text{Velocity Gradient} = \frac{\Delta V}{\Delta y} \]

where:
- \(\Delta V\) is the relative velocity between the two layers,
- \(\Delta y\) is the perpendicular distance between the layers.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Relative velocity (\(\Delta V\)) = 10 cm/s
- Perpendicular distance (\(\Delta y\)) = 0.2 cm

2. **Convert Units (if necessary):**
- Since both values are in centimeters, we can directly use them in the formula without conversion.

3. **Substitute the Values into the Formula:**
\[ \text{Velocity Gradient} = \frac{\Delta V}{\Delta y} = \frac{10 \, \text{cm/s}}{0.2 \, \text{cm}} \]

4. **Calculate the Velocity Gradient:**
\[ \text{Velocity Gradient} = \frac{10}{0.2} = 50 \, \text{s}^{-1} \]

5. **Final Answer:**
The velocity gradient between the two layers of water is \(50 \, \text{s}^{-1}\).