Find the height of a water column when the pressure at the bottom of the column is 297 kPa

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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**Problem Statement:**

Find the height of a water column when the pressure at the bottom of the column is 297 kPa.

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This problem requires us to determine the height of a column of water given a specific pressure exerted at the bottom of the column. The pressure is provided in kilopascals (kPa). The relationship between pressure, height, and density in a fluid column can be understood through the equation:

\[ P = \rho \cdot g \cdot h \]

Where:
- \( P \) is the pressure at the bottom of the column (in pascals, but given here in kilopascals)
- \( \rho \) is the density of the fluid (water, which is typically 1000 kg/m\(^3\) at standard conditions)
- \( g \) is the acceleration due to gravity (approximately 9.81 m/s\(^2\))
- \( h \) is the height of the fluid column (in meters)

To find the height \( h \), the formula can be rearranged as:

\[ h = \frac{P}{\rho \cdot g} \] 

Substitute the given pressure and known values into this equation to solve for \( h \).

**Note:** Ensure to convert the pressure from kilopascals to pascals for consistency in SI units (1 kPa = 1000 Pa).

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This explanation would assist students in understanding how to approach solving this type of problem using fluid mechanics principles.
Transcribed Image Text:**Problem Statement:** Find the height of a water column when the pressure at the bottom of the column is 297 kPa. --- This problem requires us to determine the height of a column of water given a specific pressure exerted at the bottom of the column. The pressure is provided in kilopascals (kPa). The relationship between pressure, height, and density in a fluid column can be understood through the equation: \[ P = \rho \cdot g \cdot h \] Where: - \( P \) is the pressure at the bottom of the column (in pascals, but given here in kilopascals) - \( \rho \) is the density of the fluid (water, which is typically 1000 kg/m\(^3\) at standard conditions) - \( g \) is the acceleration due to gravity (approximately 9.81 m/s\(^2\)) - \( h \) is the height of the fluid column (in meters) To find the height \( h \), the formula can be rearranged as: \[ h = \frac{P}{\rho \cdot g} \] Substitute the given pressure and known values into this equation to solve for \( h \). **Note:** Ensure to convert the pressure from kilopascals to pascals for consistency in SI units (1 kPa = 1000 Pa). --- This explanation would assist students in understanding how to approach solving this type of problem using fluid mechanics principles.
Expert Solution
Step 1

Given,

Pressure at the bottom, P=297 KPa

the density of the water, ρ=1000 Kg/m3

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