To convert 1 mm of Hg into pascal, we will use the formula for pressure:
\[ P = H \times \rho \times g \]
where:
- \( P \) is the pressure in pascals (Pa),
- \( H \) is the height of the fluid column in meters (m),
- \( \rho \) is the density of the fluid in kilograms per cubic meter (kg/m³),
- \( g \) is the acceleration due to gravity in meters per second squared (m/s²).
### Step-by-Step Solution:
**Step 1: Convert height from mm to meters.**
- Given \( H = 1 \, \text{mm} \).
- To convert mm to meters, we use the conversion factor \( 1 \, \text{mm} = 10^{-3} \, \text{m} \).
- Therefore, \( H = 1 \, \text{mm} = 1 \times 10^{-3} \, \text{m} = 0.001 \, \text{m} \).
**Step 2: Identify the values for density and gravity.**
- Given \( \rho = 13.6 \times 10^{3} \, \text{kg/m}^3 \) (density of mercury),
- Given \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity).
**Step 3: Substitute the values into the pressure formula.**
- Now, substitute \( H \), \( \rho \), and \( g \) into the pressure formula:
\[ P = H \times \rho \times g \]
\[ P = (0.001 \, \text{m}) \times (13.6 \times 10^{3} \, \text{kg/m}^3) \times (9.8 \, \text{m/s}^2) \]
**Step 4: Calculate the pressure.**
- Now we perform the multiplication:
\[ P = 0.001 \times 13.6 \times 10^{3} \times 9.8 \]
Calculating step-by-step:
1. \( 0.001 \times 13.6 = 0.0136 \)
2. \( 0.0136 \times 9.8 = 0.13328 \)
3. \( 0.13328 \times 10^{3} = 133.28 \, \text{Pa} \)
**Final Result:**
- Thus, \( P = 133.28 \, \text{Pa} \).
### Conclusion:
1 mm of mercury is equal to 133.28 pascals.
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