Find the absolute pressure in kPa at a depth of 12 m below the free surface of oil of sp. gr. 0.75 if the barometric reading is 74v0 mmHg.


To find the absolute pressure at a depth of 12 m below the surface of the oil, we can follow these steps:

### Step 1: Understanding the Formula for Pressure
The total absolute pressure \(P_{\text{abs}}\) at a depth in a fluid is given by:

\[
P_{\text{abs}} = P_{\text{atm}} + \rho g h
\]

Where:
- \(P_{\text{atm}}\) is the atmospheric pressure (from the barometric reading).
- \(\rho\) is the density of the fluid (oil in this case).
- \(g\) is the acceleration due to gravity (approximately \(9.81 \, \text{m/s}^2\)).
- \(h\) is the depth below the fluid surface.

### Step 2: Convert the Barometric Reading to kPa
The barometric reading is given as \(740 \, \text{mmHg}\). To convert this to kilopascals (kPa), we use the conversion factor:

\[
1 \, \text{mmHg} = 0.133322 \, \text{kPa}
\]

Thus, the atmospheric pressure in kPa is:

\[
P_{\text{atm}} = 740 \, \text{mmHg} \times 0.133322 \, \text{kPa/mmHg} = 98.65728 \, \text{kPa}
\]

### Step 3: Calculate the Density of Oil
The specific gravity of oil is 0.75. Since the specific gravity is the ratio of the fluid's density to the density of water, we can calculate the density of oil as:

\[
\rho_{\text{oil}} = 0.75 \times 1000 \, \text{kg/m}^3 = 750 \, \text{kg/m}^3
\]

### Step 4: Calculate the Gauge Pressure Due to the Oil Column
The pressure due to the depth of the oil column is given by:

\[
P_{\text{oil}} = \rho_{\text{oil}} \times g \times h
\]

Where:
- \(\rho_{\text{oil}} = 750 \, \text{kg/m}^3\),
- \(g = 9.81 \, \text{m/s}^2\),
- \(h = 12 \, \text{m}\).

Substituting these values:

\[
P_{\text{oil}} = 750 \times 9.81 \times 12 = 88290 \, \text{Pa} = 88.29 \, \text{kPa}
\]

### Step 5: Calculate the Absolute Pressure
Finally, the absolute pressure is the sum of the atmospheric pressure and the pressure due to the oil column:

\[
P_{\text{abs}} = P_{\text{atm}} + P_{\text{oil}} = 98.65728 \, \text{kPa} + 88.29 \, \text{kPa} = 186.94728 \, \text{kPa}
\]

### Answer:
The absolute pressure at a depth of 12 m below the surface of the oil is approximately:

\[
P_{\text{abs}} = 186.95 \, \text{kPa}
\]

Do you want further details or have any questions?

Here are five questions that build on this topic:
1. How would the pressure change if the specific gravity of the oil increased?
2. What is the gauge pressure at the same depth in water instead of oil?
3. How does the depth of the fluid affect the absolute pressure?
4. What is the significance of atmospheric pressure in calculating absolute pressure?
5. How can you calculate pressure at different depths in different liquids?

**Tip:** Always make sure to convert all units to a consistent system before performing calculations to avoid errors.

Find the absolute pressure in kPa at a depth of 12 m below the free surface of oil of sp. gr. 0.75 if the barometric reading is 740 mmHg.

Find the absolute pressure at a depth of 12 m below the free surface of oil with a specific gravity of 0.75. Convert the barometric reading from 740 mmHg to kPa and use the hydrostatic pressure formula. Step-by-step solution included. Suitable for undergraduate engineering or physics students.

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