What is the pressure at the bottom of a water tank with a cross section of 10 ft² and filled with water to a depth of 40 ft?

What is the pressure at the bottom of a water tank with a cross section of 10 ft² and filled with water to a depth of 40 ft?

• A. 10 psi
• B. 20 psi
• C. 17 psi
• D. 30 psi

Answer: (C)

To determine the pressure at the bottom of a water tank, we use the hydrostatic pressure formula, which is derived from the principles of fluid mechanics. The pressure exerted by a fluid at a certain depth is given by the formula: \[ P = \rho \cdot g \cdot h \] Where: - \( P \) is the pressure at the depth (in pounds per square foot, or psi), - \( \rho \) 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), but this is often factored into the density for convenience, - \( h \) is the depth of the fluid (in feet). In this scenario, since we only need the pressure in psi, we can simplify our calculation for a column of water, where we can consider the pressure increase of water at standard conditions. First, we know that at a depth of 1 foot, the pressure is approximately 0.433 psi (since 1 psi equals about 2.31 feet of water). Therefore, at a depth of 40 feet, the pressure can be calculated as

To determine the pressure at the bottom of a water tank, we use the hydrostatic pressure formula, which is derived from the principles of fluid mechanics. The pressure exerted by a fluid at a certain depth is given by the formula:

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

Where:

• ( P ) is the pressure at the depth (in pounds per square foot, or psi),

• ( \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), but this is often factored into the density for convenience,

• ( h ) is the depth of the fluid (in feet).

In this scenario, since we only need the pressure in psi, we can simplify our calculation for a column of water, where we can consider the pressure increase of water at standard conditions.

First, we know that at a depth of 1 foot, the pressure is approximately 0.433 psi (since 1 psi equals about 2.31 feet of water). Therefore, at a depth of 40 feet, the pressure can be calculated as