We are asked to find the pressure in the pipe for a manometer setup, which involves the use of specific gravity, area relations, and pressure concepts. Let's break down the steps to solve the problem:

Given Information:

1. Specific gravity of the liquid in the pipe: 0.9
2. Specific weight of mercury: 13.6
3. Height of the mercury column: 40 cm (from the manometer)
4. Height difference of the liquid in the reservoir: 20 cm
5. The area of the reservoir is 100 times the area of the tube.

Formula for pressure in a manometer:

The pressure in the pipe $P_{pipe}$ can be found using the equation:

$P_{pipe} = P_0 + \rho_{fluid} g h_{fluid} - \rho_{mercury} g h_{mercury}$

Where:

• $P_0$ is the atmospheric pressure.
• $\rho_{fluid}$ is the density of the liquid in the pipe (based on its specific gravity).
• $g$ is the acceleration due to gravity (which cancels out).
• $h_{fluid}$ is the height difference of the liquid in the reservoir (20 cm).
• $h_{mercury}$ is the height of the mercury column (40 cm).
• $\rho_{mercury}$ is the density of mercury, which is 13.6 times the density of water.

Conversion:

• Specific gravity $SG$ is the ratio of the density of a substance to the density of water. So, the density of the liquid in the pipe is $\rho_{fluid} = 0.9 \times \rho_{water}$.
• The pressure will be calculated as the difference between the pressure due to the liquid column and the pressure due to the mercury.

Now, I will calculate the pressure in the pipe.The pressure in the pipe, relative to atmospheric pressure, is approximately 51,600.6 Pascals (Pa).

Would you like further details or have any other questions?

Here are five related questions to expand your understanding:

1. How does the specific gravity of a fluid affect the pressure in a manometer?
2. How can we calculate the absolute pressure in the pipe if atmospheric pressure is known?
3. Why does the height of the mercury column play a significant role in manometer readings?
4. How would the pressure change if the specific gravity of the liquid in the pipe increased?
5. What other devices are used to measure fluid pressure besides a manometer?

Tip: Remember, the specific gravity of a fluid is dimensionless, and it represents how dense the fluid is compared to water. This ratio is crucial when calculating pressure in fluid systems.