https://file.aiquickdraw.com/mathbot/file/172882572979017lr6t3t.jpg

The image presents the following problem:

---

**Q.2 Using a UTI gauge from the ullage port, a box-shaped cargo oil tank (dimensions 20 m × 11.5 m) registered an oil dip of 27 cm with a water cut of 10 cm on arrival at the loading terminal. Calculate the OBQ (On Board Quantity).**

- **Tank dimensions:** 20 m × 11.5 m
- **Oil dip:** 27 cm
- **Water cut:** 10 cm
- **Trim:** 3 m (unclear context from the image)
- **Ullage port is located 6.37 m forward of the after bulkhead.**

---

To calculate the OBQ (On Board Quantity), we need to consider both the oil and water layers. Here's the breakdown:

1. **Oil Dip**: 27 cm (total height of the oil and water in the tank).
2. **Water Cut**: 10 cm (height of the water layer).
   
   This means the oil depth is \(27 - 10 = 17 \, \text{cm}\).

3. **Volume of water**: \( \text{Area of the tank} \times \text{height of the water} \).

   - Area of the tank base: \( 20 \, \text{m} \times 11.5 \, \text{m} = 230 \, \text{m}^2 \).
   - Volume of water: \( 230 \, \text{m}^2 \times 0.10 \, \text{m} = 23 \, \text{m}^3 \).

4. **Volume of oil**: Similarly, calculate the volume for the oil layer.

   - Volume of oil: \( 230 \, \text{m}^2 \times 0.17 \, \text{m} = 39.1 \, \text{m}^3 \).

5. **Total OBQ**: The total On Board Quantity is the sum of the oil and water volumes:
   \[
   \text{OBQ} = 39.1 \, \text{m}^3 + 23 \, \text{m}^3 = 62.1 \, \text{m}^3.
   \]

Thus, the OBQ is approximately **62.1 m³**.

---

Would you like a more detailed explanation or further clarifications?

Here are some follow-up questions you might find useful:

1. How does trim affect the measurement of OBQ in different tank geometries?
2. What is the significance of the "ullage port" in measuring OBQ?
3. Could other factors like temperature or density adjustments be necessary in OBQ calculations?
4. How would the calculation change for non-box-shaped tanks?
5. What are the common methods for reducing errors in OBQ measurements?

**Tip:** Always verify ullage and dip readings at multiple points in the tank to ensure accurate OBQ calculation, especially when the trim is significant.

Q.2 Using a UTI gauge from the ullage port, a box-shaped cargo oil tank (20 m x 11.5 m) registered an oil dip of 27 cm with a water cut of 10 cm on arrival at the loading terminal. Calculate the OBQ (On Board Quantity).

Learn how to calculate the On Board Quantity (OBQ) for a box-shaped cargo oil tank using a UTI gauge. The problem involves geometry and volume calculations with measurements of oil dip, water cut, and tank dimensions. Suitable for advanced learners.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation