A vacuum chamber pressure gauge showing a reading of 40 mm Hg vacuum. Specific weight of Mercury (Hg) is 133.7kNm3133.7kNm3. The equivalent pressure is:


Question 5Answer

a.

-0.2992

b.

0.29918

c.

5348.00

d.

-5348.000

e.

5348.0

To solve this, we need to calculate the equivalent pressure from the vacuum reading.

### Given:
- Vacuum reading = 40 mm Hg
- Specific weight of Mercury (Hg) = \( 133.7 \, \text{kN/m}^3 \)

### Step-by-step solution:

1. **Convert the vacuum reading into meters**:
   \[
   40 \, \text{mm} = 0.04 \, \text{m}
   \]

2. **Calculate the equivalent pressure**:
   The formula for pressure is:
   \[
   P = h \cdot \gamma
   \]
   where:
   - \( h \) = height of the mercury column (in meters)
   - \( \gamma \) = specific weight of mercury
   
   Substituting the values:
   \[
   P = 0.04 \, \text{m} \cdot 133.7 \, \text{kN/m}^3 = 5.348 \, \text{kPa}
   \]

Thus, the equivalent pressure is \( 5.348 \, \text{kPa} \).

Since the pressure is being measured in a vacuum (negative relative to atmospheric pressure), the result should be negative.

The correct answer is:
\[
\boxed{-5348.000 \, \text{Pa}} \, (\text{option d})
\]

Would you like more details on this calculation or any other clarifications?

---

Here are 5 questions to expand on the topic:

1. How do you convert vacuum pressure into gauge pressure?
2. What is the significance of using mercury in pressure measurement?
3. Can you explain the difference between absolute pressure and gauge pressure?
4. How would the equivalent pressure change if the specific weight of mercury was different?
5. What role does atmospheric pressure play in vacuum readings?

**Tip**: Remember that vacuum pressure is always measured as a negative value because it represents a pressure lower than atmospheric pressure.

A vacuum chamber pressure gauge showing a reading of 40 mm Hg vacuum. Specific weight of Mercury (Hg) is 133.7 kN/m^3. The equivalent pressure is:

This problem involves calculating the equivalent pressure from a 40 mm Hg vacuum reading using the specific weight of mercury (133.7 kN/m^3). The detailed solution includes unit conversion and applying the pressure formula P = h * γ. Suitable for students in Grades 9-12.

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