A manometer (pressure-measuring device) uses mercury (sg=13.6) as the fluid. A reading of 5 inches on the manometer is equivalent to how many millimeters of kerosene (sg=0.82)? (2106.34146 mm

We can solve this problem by applying the principle of hydrostatic pressure, which states that the pressure exerted by a fluid column is proportional to the height of the column and the specific gravity of the fluid.

Here are the steps:

### Step 1: Pressure relation
The pressure exerted by a column of fluid is given by:
\[
P = h \cdot \text{SG} \cdot \rho_{\text{water}} \cdot g
\]
where:
- \( P \) is the pressure,
- \( h \) is the height of the fluid column,
- \( \text{SG} \) is the specific gravity of the fluid,
- \( \rho_{\text{water}} \) is the density of water (used as a reference density),
- \( g \) is the acceleration due to gravity.

Since pressure must be equal in both cases (for mercury and kerosene):

\[
h_{\text{Hg}} \cdot \text{SG}_{\text{Hg}} = h_{\text{kerosene}} \cdot \text{SG}_{\text{kerosene}}
\]

### Step 2: Convert height of mercury to kerosene
We are given:
- \( h_{\text{Hg}} = 5 \text{ inches} \),
- \( \text{SG}_{\text{Hg}} = 13.6 \) (mercury),
- \( \text{SG}_{\text{kerosene}} = 0.82 \).

First, convert 5 inches to millimeters:
\[
5 \text{ inches} = 5 \times 25.4 = 127 \text{ mm}
\]

Now use the pressure relation to find \( h_{\text{kerosene}} \):
\[
127 \cdot 13.6 = h_{\text{kerosene}} \cdot 0.82
\]

Solve for \( h_{\text{kerosene}} \):
\[
h_{\text{kerosene}} = \frac{127 \cdot 13.6}{0.82} = 2106.34 \text{ mm}
\]

### Final Answer:
The equivalent height of kerosene is approximately **2106.34 mm**.

Do you want further details or explanations on any part of the solution?

Here are 5 related questions to expand on this concept:
1. What is the relationship between pressure and fluid column height in manometry?
2. How does the specific gravity of a fluid affect the height of the column?
3. Can you convert the height of other fluids using the same method?
4. How would the height change if a fluid with a higher specific gravity than mercury was used?
5. Why is it important to use a reference fluid like water for calculating specific gravity?

**Tip:** Always ensure that units are consistent when applying pressure or height calculations in hydrostatics.

A manometer (pressure-measuring device) uses mercury (sg=13.6) as the fluid. A reading of 5 inches on the manometer is equivalent to how many millimeters of kerosene (sg=0.82)?

Learn how to convert a pressure reading of 5 inches of mercury (SG=13.6) on a manometer to millimeters of kerosene (SG=0.82) using hydrostatic pressure principles. This detailed step-by-step guide is suitable for students in Grades 10-12, covering key formulas and specific gravity calculations.

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