

Calculating Displacement
Name: Sammy
Status: Student
Age: 8
Location: N/A
Country: N/A
Date: N/A
Question:
My Dad and I are going to build a sail boat using PVC
pipes for flotation. Is there an easy way to caculate how many 8 foot
long, eight inch diameter pipes we will need to support our weight and
keep the boat floating?
Replies:
The weight that the pipes will support is the weight of the water they can
displace minus the weight of the pipes themselves. To calculate this, you
need to know the volume of the pipes, the weight of the pipes, and the
density (weight/volume) of water.
Fresh water has a density of 1 kg/liter. Salt water has a higher density.
The volume of the pipes can be calculated from their diameter and length by
the formula
V = L pi r^2, where
L is the length of the pipe, 8 ft = 96 in.,
pi = 3.14159,
r is the radius of the pipe, 4 in.
So the volume of a pipe is
V = (96 in)(3.14)(4 in)^2
= (96 in)(3.14)(16 in^2)
= 4823 in^3
Now you need to convert cubic inches to liters. 1 cubic inch = 0.01639
liters, so
;V = (4823 in^3)(0.01639 L/in^3)
= 79 L.
So, in fresh water, an 8ft length of 8in diameter PVC pipe can float 79
kg minus its own weight.
Richard E. Barrans Jr., Ph.D.
Assistant Director
PG Research Foundation, Darien, Illinois
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Update: June 2012

