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Name: Green Arrow is helping clean up some pollution from fracking. He fills
Uploaded: 2024-03-20T06:56:55.000Z
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Description: Green Arrow is helping clean up some pollution from fracking. He fills a tank with the pollutants the result is a tank filled to a depth of 21.0 cm with brackish water on top of which floats a 56.1 thick layer of crude oil. Assuming that the density

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Green Arrow is helping clean up some pollution from fracking. He fills a tank with the pollutants the result is a tank filled to a depth of 21.0 cm with brackish water on top of which floats a 56.1 thick layer of crude oil. Assuming that the density of the brackish water is 1.000 g/cm^ 3 and the density of the crude oil is 0.965 g/cm^ 3 what will be the gauge pressure (in kPa) at the bottom of the tank? Explain how you solved the problem involving a fluid-filled tank. Be sure to state what your known and unknown quantities are, what concepts were applied, and what equations were used!

**Calculating Gauge Pressure at the Bottom of a Tank Filled with Mixed Fluids**

**Problem Statement:**

Green Arrow is helping clean up some pollution from fracking. He fills a tank with the pollutants; the result is a tank filled to a depth of 21.0 cm with brackish water on top of which floats a 56.1 cm thick layer of crude oil.

Assuming that the density of the brackish water is 1.000 g/cm³ and the density of the crude oil is 0.965 g/cm³, what will be the **gauge pressure** (in kPa) at the bottom of the tank?

**Solution Approach:**

To determine the gauge pressure at the bottom of the tank, we can use the formula for the pressure exerted by a fluid column:

\[ P = \rho g h \]

Where:
- \( P \) is the pressure
- \( \rho \) is the density of the fluid
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \))
- \( h \) is the height of the fluid column

Since there are two fluids involved, we will find the pressure due to each fluid column separately and then sum them to get the total gauge pressure at the bottom of the tank.

1. **Pressure due to brackish water:**
- Density (\( \rho_{water} \)) = 1.000 g/cm³ = 1000 kg/m³
- Height (\( h_{water} \)) = 21.0 cm = 0.210 m

\[ P_{water} = \rho_{water} \cdot g \cdot h_{water} \]
\[ P_{water} = 1000 \, \text{kg/m}^3 \times 9.81 \, \text{m/s}^2 \times 0.210 \, \text{m} \]
\[ P_{water} = 2056.1 \, \text{Pa} \]

2. **Pressure due to crude oil:**
- Density (\( \rho_{oil} \)) = 0.965 g/cm³ = 965 kg/m³
- Height (\( h_{oil} \)) = 56.1 cm = 0.

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