Fluid Pressure
The term fluid pressure is coined as, the measurement of the force per unit area of a given surface of a closed container. It is a branch of physics that helps to study the properties of fluid under various conditions of force.
Gauge Pressure
Pressure is the physical force acting per unit area on a body; the applied force is perpendicular to the surface of the object per unit area. The air around us at sea level exerts a pressure (atmospheric pressure) of about 14.7 psi but this doesn’t seem to bother anyone as the bodily fluids are constantly pushing outwards with the same force but if one swims down into the ocean a few feet below the surface one can notice the difference, there is increased pressure on the eardrum, this is due to an increase in hydrostatic pressure.
![**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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc463f08e-ec7e-4810-a9a2-5563bca4d00b%2Fd835aee9-80a6-4503-ae3c-07edefa83dc5%2Fkgq3f9_processed.jpeg&w=3840&q=75)
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Given,
Pressure at the bottom,
the density of the water,
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