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.