Question

A housing tract is located at an approximate average elevation of \(2,225 \mathrm{ft}\) above sea level and is served from a storage tank that is at \(2,330 \mathrm{ft}\). The average head loss from the tank to the housing tract is \(15.5\) psi. What is the minimum water level in the tank to maintain a minimum pressure 40 psi?

Short answer

233.205 ft

Step-by-step solution

Convert PSI to Feet of Water

First we need to convert the pressure from psi to feet of water. The conversion factor is 2.31 feet of water per psi. We need to convert both the head loss and the minimum pressure required.\[\text{Head loss in feet} = 15.5 \text{ psi} \times 2.31 \frac{\text{feet}}{\text{psi}} = 35.805 \text{ ft}\]\[\text{Minimum pressure in feet} = 40 \text{ psi} \times 2.31 \frac{\text{feet}}{\text{psi}} = 92.4 \text{ ft}\]

Determine Elevation Difference

Calculate the difference between the elevation of the storage tank and the housing tract:\[\text{Elevation difference} = 2330 \text{ ft} - 2225 \text{ ft} = 105 \text{ ft}\]

Calculate Total Head Required at Housing Tract

Determine the total head required at the housing tract, which includes the minimum pressure head and the head loss:\[\text{Total head required} = 92.4 \text{ ft} + 35.805 \text{ ft} = 128.205 \text{ ft}\]

Calculate Minimum Water Level in Tank

Finally, calculate the necessary water level in the tank by adding the total head required to the difference in elevation:\[\text{Minimum water level in tank} = 105 \text{ ft} + 128.205 \text{ ft} = 233.205 \text{ ft}\]

Key concepts

head loss

Head loss is the reduction in total pressure or head in a fluid flow system due to friction and other resistance factors. It is important in understanding how much energy is lost as water travels through pipes. This lost energy impacts how well water can be delivered from one point to another. Head loss is often measured in terms of pressure (psi) but can also be expressed in feet of water for easier calculations. This helps in determining how much additional pressure (or head) is needed to compensate for these losses.

elevation difference

Elevation difference refers to the vertical height difference between two points in a fluid system. In water pressure calculations, it is crucial because the height or elevation affects the potential energy of the water, which then converts to pressure. For example, if a water tank is situated at a height of 2330 ft above sea level and houses are at 2225 ft, the elevation difference is 105 ft. This difference directly contributes to the available pressure to push water down to the housing tract. Always remember to measure elevation difference in consistent units, usually feet, to make the calculations straightforward.

conversion factors

Conversion factors simplify the process of translating measurements from one unit to another. In water pressure calculations, one valuable conversion factor is that 1 psi equals 2.31 feet of water. This enables us to convert pressure readings from psi (pounds per square inch) into feet of water, a more intuitive unit for measuring height or water level. For instance, converting a head loss of 15.5 psi into feet of water involves multiplying by 2.31:\[ \text{Head loss in feet} = 15.5 \text{ psi} \times 2.31 \frac{\text{ft}}{\text{psi}} = 35.805 \text{ ft} \]Similarly, to maintain a minimum pressure of 40 psi, convert it to feet:\[ \text{Minimum pressure in feet} = 40 \text{ psi} \times 2.31 \frac{\text{ft}}{\text{psi}} = 92.4 \text{ ft} \]

minimum pressure

Minimum pressure is the least amount of pressure required at a particular point in a water distribution system to ensure proper functioning. In residential areas, a common minimum pressure requirement is 40 psi, which ensures that all households receive adequate water pressure for daily use. To find the necessary water level in a storage tank, you must factor in this minimum pressure. First, convert the required minimum pressure to feet of water using the known conversion factor (2.31 feet per psi). Then add this to the head loss and elevation difference. This conversion is crucial because it helps in calculating the total head required to meet the system's pressure needs.

feet of water

Feet of water is a unit of measurement that translates pressure into an equivalent height of a water column. It is particularly useful for calculating how much pressure a specific elevation of water can generate or how much pressure is lost due to friction in pipes. For example, if the head loss is 15.5 psi, converting it to feet of water makes it more tangible:\[ 15.5 \text{ psi} \times 2.31 \frac{\text{feet}}{\text{psi}} = 35.805 \text{ feet} \]Similarly, minimum required pressure also needs to be converted into feet of water. Therefore, understanding and using feet of water helps in visualizing and planning the water distribution system more accurately.