# 7.1: Pressure

$$\newcommand{\vecs}{\overset { \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}{\| #1 \|}$$ $$\newcommand{\inner}{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

Pressure is related to the vertical distance from the surface of water to a reference point somewhere below the water surface typically expressed in feet. For example, a water storage tank has a certain water level inside of it. The reference point below could be a water faucet a certain distance in feet below the water level. This distance in feet is the head pressure (in feet). The other common unit for pressure is POUNDS PER SQUARE INCH, (psi). You can convert back and forth between feet and pounds per square inch using one of the following conversion factors.

$1 \text { foot }=0.433 \mathrm{psi} \quad \text { or } \quad 1 \mathrm{psi}=2.31 \text { feet } \nonumber$

To stay consistent with UDA, view the following conversion factors as

$\dfrac{1 \text { foot }}{0.433 \text { psi }} \quad \text { or } \quad \dfrac{1 \text { psi }}{2.31 \text { feet }} \nonumber$

Remember, as with all conversion factors, these can be written as the inverse.

$\dfrac{0.433 \mathrm{psi}}{1 \mathrm{foot}} \quad \text { or } \quad \dfrac{2.31 \text { feet }}{1 \mathrm{psi}} \nonumber$

Example $$\PageIndex{1}$$ Figure $$\PageIndex{1}$$
1. Assume both cylinders above are filled with water, which one has a greater pressure at the base of it?
2. What is the pressure at the base of each cylinder?

Solution

1. The answer is neither! The pressure at the base of each cylinder is the same because the height of the water is the same.
2. $$\dfrac{30 \text { feet }}{1} \times \dfrac{1 \mathrm{psi}}{2.31 \mathrm{feet}}=12.98 \mathrm{psi}$$ or (if you round) $$13 \mathrm{psi}$$

## Exercise 7.1

Calculate the following pressure problems

1. What is the pressure in psi at the bottom of a 30 foot tall tank if it is full?
2. What is the pressure in feet if the psi is 130?
3. A storage tank is 45 feet tall and half full. What is the pressure in psi?
4. A water tank sits on a 50 foot hill and is 25 feet tall. Assuming the tank is full, what is the pressure in psi at the bottom of the hill?
5. A fire hydrant was hit and water is spraying up approximately 75 feet. What is the approximate pressure in psi?

7.1: Pressure is shared under a CC BY license and was authored, remixed, and/or curated by LibreTexts.