Understanding Fluid Pressure at Depth in a Cylindrical Container

Introduction

Understanding the principles of fluid pressure at different depths is crucial for various applications in engineering, hydrology, and physics. This article delves into how to calculate the pressure exerted by a fluid with a specific gravity of 1.7 at a depth of 15 meters within a closed cylindrical container. We will explore the formula and method to perform this calculation, providing a detailed step-by-step guide.

Calculation of Fluid Pressure

When a fluid is filled in a closed cylindrical container, the pressure exerted at a certain depth can be calculated using a straightforward formula. The formula for calculating the pressure exerted by a fluid is given by:

$$ P rho cdot g cdot h $$

Where:

P is the pressure (in Pascals, Pa) ρ (rho) is the density of the fluid (in kg/m3) g is the acceleration due to gravity (approximately 9.81 m/s2) h is the depth of the fluid (in meters, m)

Step-by-Step Calculation

Step 1: Find the Density of the Fluid

The specific gravity (SG) of a fluid is the ratio of its density to the density of water. The density of water is approximately 1000 kg/m3. Therefore, the density of the fluid can be calculated as follows:

$$ rho text{SG} times text{density of water} 1.7 times 1000 , text{kg/m}^3 1700 , text{kg/m}^3 $$

Step 2: Calculate the Pressure

Now, we substitute the values into the pressure formula:

$$ P 1700 , text{kg/m}^3 times 9.81 , text{m/s}^2 times 15 , text{m} $$

Calculating this gives:

$$ P 1700 times 9.81 times 15 $$ $$ P approx 250155 , text{Pa} $$

To convert this to kilopascals (kPa):

$$ P approx 250.155 , text{kPa} $$

Step 3: Understanding the Context

Lets consider the container to have the same volume at any depth. For constant temperature, we will have no changes due to changes in vapor pressure. Most liquids, due to their high density, are considered incompressible.

Even though the surroundings will exert pressure on the container as a function of the depth of the water column, the container maintains a constant volume. As the temperature is also constant, the pressure exerted by the fluid in the container does not change. This is similar to the experience we have when diving into water.

Real-World Application

Imagine the base of the cylinder had an area of 1 m2. At a depth of 15 meters, you would have a total of 15 m3 of fluid in the tank. The mass of this fluid would be:

$$ text{Mass} 15 , text{m}^3 times 1000 , text{L/m}^3 times 1.7 , text{kg/L} 25500 , text{kg} $$

The weight of this mass of fluid would be:

$$ text{Weight} 25500 , text{kg} times 9.81 , text{N/kg} 250155 , text{N} $$

Over an area of 1 m2, the pressure would be:

$$ text{Pressure} 250155 , text{N/m}^2 250155 , text{Pa} 250.155 , text{kPa} $$

Conclusion

By understanding the principles of fluid pressure and using the appropriate formula, we can accurately calculate the pressure exerted by a fluid in a closed cylindrical container. This knowledge is essential for a variety of practical applications, including engineering, hydrology, and environmental science.

Deepening our knowledge of fluid mechanics can provide valuable insights into many real-world scenarios. Whether you are a student, a professional, or simply interested in learning more about physics, these principles offer a fascinating and practical field of study.