How to Calculate Pounds per Linear Inch

Pressure is defined as a way of describing force per unit area. It is often important to specify pressures for liquids or gases, and there are several different units that can describe pressure.

Some pressures are instead a force per unit length, as is the case for pounds per linear inch (PLI). This quantity could also be considered a weight density. It is important to remember that pounds is a unit of force that describes the force of gravity on an object.

A similar unit to PLI is pounds per square inch (PSI). Because the dimensions of these quantities are different, you cannot convert PLI to PSI. Furthermore, you cannot convert a unit of PSI to pounds; this operation requires an operation that cancels the area dimension, meaning it has to be multiplied by an area.

How to Determine Pounds per Linear Inch

Imagine you have a rope that is uniform in density and is 10 feet long. The whole rope weighs 5 pounds. The linear weight density is therefore 5 pounds / 10 feet, or 0.5 pounds per foot. To convert this to pounds per linear inch, use the conversion of feet to inches: 1 foot = 12 inches. That means that density of the rope is 0.041 pounds per linear inch.

There may be unique problems in which pressure is given in PSI, which has units of pounds per square inch, that requires multiplying the pressure by length. In doing so, one power of inches in the denominator is reduced, and you are left with pounds per linear inch.

There are many ways that one can calculate PLI and PSI, but more commonly you will know the pressure or weight density of some material.

How to Use PSI to Safely Buy a Couch

PSI and PLI are units of pressure and weight density that are most commonly used in engineering and construction. Therefore, it may be handy to understand how to calculate PSI or PLI when constructing a structure that needs to support weight. Or in the following example, you will see how knowing the PSI tolerance of a structure can inform important safety concerns.

Imagine you are buying some furniture for your porch. You will need to know how much weight the porch can support so that you can purchase sturdy furniture, without breaking the floorboards. Remember that people will likely occupy the furniture, so you want to make sure that the furniture is heavy, but not so heavy that if someone sits on it the porch breaks.

The information that you are given is that the maximum PSI that the porch can support is 10 PSI and that the total area of your porch is 160 square feet.

If the bench that you are interested in purchasing is made from solid hardwood, and the dimensions of the base that will rest on the porch is 3 feet by 8 feet. The area is 24 square feet. The manufacturer label states that the bench weighs 300 pounds.

You can determine the PSI that the bench will apply to the boards from this information: The area in inches is 3,456 in2, so the PSI applied by the bench is 300 pounds/ 3,456 in2, or 0.09 PSI. This is significantly less than 10 PSI, so the bench is safe to place on the porch, and many people can safely sit on it.

What Is a PSI Converter?

This is a general term, but it could mean two things:

1) A PSI converter could use a given PSI threshold, and an area, to determine the resulting force in pounds. Just as you did in the earlier example, you could use a PSI converter to determine the maximum weight a structure could support.

2) PSI is not the metric unit for pressure; Newtons per square meter would be the SI unit. Therefore a PSI converter could convert from PSI to N/m2.

To convert from PSI to N/m, you can use the following conversions: 1 pound (lbs) = 4.448 Newtons and 1 inch = 2.54 centimeters. Further, there are 100 centimeters in a meter. Therefore 1 PSI is 6882.01 N/m2.

References

About the Author

Lipi Gupta is currently pursuing her Ph. D. in physics at the University of Chicago. She earned her Bachelor of Arts in physics with a minor in mathematics at Cornell University in 2015, where she was a tutor for engineering students, and was a resident advisor in a first-year dorm for three years. With this experience, when not working on her Ph. D. research, Gupta participates in STEM outreach activities to promote young women and minorities to pursue science careers.

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