Firefighter Math: 4.7 Graphs

Graphing is a method of showing the relationship between two or more sets of data by means of a chart or sketch. Trends in data are easier to identify with a graph than a data table.

A graph can be created using graphing paper (you purchase gridded paper or draw your own), a computer application such as Excel, or graphing applications for a personal digital assistant (PDA) or phone. A graph shows a set of data points plotted in relation to the horizontal axis and vertical axis. 

Example 1 - Draw a graph for pump performance showing the relationship between pressure (psi) and flow (gpm). Use the following table of pump performance data values. 

 

Step 1. Pump performance charts are typically drawn with the flow on the horizontal axis and pressure on the vertical axis. Label the horizontal axis as flow in gallons per minute. Label the vertical axis as pressure in pounds per square inch.


Step 2. Mark the horizontal axis from 0 to 90 in even increments. Mark the vertical axis from 0 to 300 in even increments of 25 pounds per square inch, as the data points were collected in increments of 25 pounds per square inch.

Step 3. Plot each data set by finding the pressure value on the vertical axis and then the flow value on the horizontal axis. Mark (plot) a point where the two values meet. Continue plotting points for all data sets.

Step 4. Run a curved line through the points. Not all the points will be on the curve, some of the points will lie above the line and some below. Special statistical calculations are used to determine how far off the curve a data point can be and still be meaningful. Typically, if the point is off the curve enough to affect the shape of the curve, the data set should be rerun.


 

USING A GRAPH TO FIND APPROXIMATE VALUES

A curve can be used to find approximate values for data in between the data sets collected. The curve can also be used to show performance trends. For example, this curve shows that as pressure is decreasing, the flow rate increases proportionally throughout the range of performance. 

Example 2 - Using the graph above, find the indicated flow rate at a pressure of 263 pounds per square inch (psi).

Step 1. Approximate the location of 263 pounds per square inch on the pressure axis. This location is approximately halfway between 275 and 250 pounds per square inch.

Step 2. Move horizontally until the curved line is met.

Step 3. Move vertically from the curved line to the flow rate axis. Read or approximate the flow rate.
 

The flow rate at 263 psi is 35 gallons per minute.
 

DETERMINING THE SLOPE OF A CURVE

The slope of a line can be determined from a plot using the slope formula.

slope = rise/run

Example 3 - Find the slope of the line drawn on the plot above for the interval between 50 and 150 pounds per square inch.
It's important to be aware what interval is being used, because the line drawn is a curve and the slope will change with each section of line.

Note from the curve that as the pressure varies from 50 to 150 pounds per square inch, the the flow rate varies from about 79 to 63 gallons per minute.

Pressure, pounds per square inch, is on the vertical axis, so it is the rise. Flow rate, gallons per minute, is on the horizontal axis, so it is the run.

Slope = rise / run = ((150 - 50) psi / 63 - 79) gpm = 100 psi / (-16 gpm) = -6 psi/gpm

The slope is -6 psi/gpm. The negative slope indicates that as the horizontal value (flow rate) increases, the vertical value (pressure) pressure decreases.
 

READING DISTANCE FROM A MAP CHART

Maps are generally broken into grids and labeled on the vertical and horizontal axes for ease of locating places or numbers. If the vertical and horizontal values are known, the area on the map can be obtained by finding where the two lines intersect or cross. Charts accompanying the map provide information about the distance between different map locations. By reading the appropriate values from those horizontal and vertical axes.

Example 4 - Use the mileage chart below to find the distance between Tampa, FL, and Albuquerque, NM.



Step 1. Locate Tampa on the horizontal axis. Draw a vertical line through these grids.

Step 2. Locate Albuquerque on the horizontal axis. Draw a horizontal line across these grids.

Step 3. Read the mileage amount where the two lines cross



The distance between Tampa and Albuquerque is 1,760 miles.