A column of water is 10 ft. Exerts a pressure of how many ft per sq in at the base?
The Correct Answer and Explanation is :
To determine the pressure exerted by a column of water, we can use the hydrostatic pressure formula, which states that pressure (P) at a depth (h) in a fluid is given by:
[
P = \rho \cdot g \cdot h
]
Where:
- ( P ) is the pressure,
- ( \rho ) is the density of the fluid (for water, approximately 62.4 lb/ft³),
- ( g ) is the acceleration due to gravity (approximately 32.2 ft/s²), and
- ( h ) is the height of the fluid column (in this case, 10 ft).
First, we can find the pressure at the base of the column of water:
- Calculate the pressure in pounds per square foot (psf):
[
P = 62.4 \, \text{lb/ft}³ \cdot 10 \, \text{ft} = 624 \, \text{lb/ft}²
] - Convert from pounds per square foot (psf) to pounds per square inch (psi):
To convert psf to psi, we need to know that there are 144 square inches in a square foot (since ( 1 \, \text{ft}^2 = 12 \, \text{in} \times 12 \, \text{in} = 144 \, \text{in}^2 )):
[
P = \frac{624 \, \text{lb/ft}²}{144 \, \text{in}²/\text{ft}²} \approx 4.33 \, \text{psi}
]
Therefore, a 10 ft column of water exerts a pressure of approximately 4.33 psi at its base.
Explanation
This calculation shows how hydrostatic pressure increases with depth in a fluid. The weight of the water column above the base generates pressure due to gravity acting on the mass of the water. Hydrostatic pressure is a fundamental principle in fluid mechanics, reflecting that pressure is exerted equally in all directions at a given depth.
The density of water is crucial in these calculations, as it directly influences the amount of pressure exerted at any height. In real-world applications, understanding this pressure is essential for designing water systems, predicting flood behavior, and assessing structural integrity in hydraulic engineering. Additionally, similar principles apply to other fluids, where variations in density will result in different pressures exerted at the same height.