Question

A home sits at an elevation of \(1,301 \mathrm{ft}\) above sea level. The base of a water tank that serves the home sits at an elevation of \(1,475 \mathrm{ft}\) above sea level. The tank is 35 feet tall and \(3 / 4\) full. What is the pressure in psi at the home?

Short answer

86.21 psi

Step-by-step solution

Understand the Problem

The home and the base of the water tank are at different elevations. The tank is partially full, and we need to calculate the water pressure at the home in psi.

Calculate the Elevation Difference

Determine the difference in elevation between the base of the water tank and the home: Elevation of tank base: 1,475 ft Elevation of home: 1,301 ft Difference in elevation = 1,475 ft - 1,301 ft = 174 ft

Calculate Height of Water in the Tank

Since the tank is 35 feet tall and is 3/4 full: Height of water = 3/4 * 35 ft = 26.25 ft

Determine the Total Water Column Height

Add the height of the water in the tank to the elevation difference: Total water column height = 174 ft + 26.25 ft = 200.25 ft

Convert Height to Pressure

Use the formula to convert the height of the water column to pressure in psi. The formula is: Pressure (psi) = Water column height (feet) * 0.433 Pressure = 200.25 ft * 0.433 = 86.20825 psi

Key concepts

elevation difference

When determining water pressure, understanding the elevation difference is crucial. In our exercise, the elevation difference is the height difference between the base of the water tank and the home.

This is calculated by subtracting the elevation of the home from the elevation of the tank's base.

This ensures we consider how gravity impacts the water flow.

The greater the difference, the more pressure can build as water travels downward.

For example, in the exercise, the elevation difference is calculated as follows:

Elevation of tank base: 1,475 ft
Elevation of home: 1,301 ft
Difference in elevation = 1,475 ft - 1,301 ft = 174 ft

water column height

Calculating the water column height involves adding the height of water in the tank to the elevation difference.

The water column height represents the total vertical distance that the water must travel from the tank to the home.

First, determine the height of the water in the tank. In the problem provided, the tank is 35 feet tall and is 3/4 full:

Height of water = (3/4) * 35 ft = 26.25 ft

Next, add this height to the elevation difference:

Total water column height = Elevation Difference + Height of water column
Total water column height = 174 ft + 26.25 ft = 200.25 ft

This total height helps us calculate the pressure exerted by the water.

pressure conversion formula

To find the water pressure at the home's elevation, we use a standard conversion formula, where we convert the height of a water column into pressure in psi (pounds per square inch).

The formula is simple:

Pressure (psi) = Water column height (ft) * 0.433

In our exercise, the total water column height is 200.25 ft. So, using the formula, we get:

Pressure (psi) = 200.25 ft * 0.433 = 86.20825 psi

This means the pressure at the home's elevation due to the water column is approximately 86.21 psi.

This formula helps in understanding how high water columns translate to pressure levels in practical situations. Using these steps, you can solve similar problems by just plugging in your values.