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Pascal's Principle
Name: David
Status: other
Grade: other
Location: CA
Country: N/A
Date: 8/17/2005
Question:
When I stand on a collapsible water container with a
rigid flat surface on top for even weight distribution, water only rises
a few feet above the container with a 1/2 inch ID hose. I weigh
approximately 170 pounds. Is it possible to get the water to rise above
my head using my body weight?
Replies:
David,
Liquids depend more on pressure than weight. If your body weight were
distributed over a smaller area, you would be exerting more pressure on the
water below you. This greater pressure would result in the water rising
higher in the hose. Remember, pressure is force divided by the area over
which it is distributed. A narrower water container and rigid surface would
be the way to go.
Dr. Ken Mellendorf
Physics Instructor
Illinois Central College
It is indeed and I just did it! Remember that it is the pressure that
counts and NOT the force. Pressure is force per unit area, so if you have a
given force acting over a small area, you can make the pressure very large.
The relevant equation is p = rgh, where p is the pressure in Newtons/m^2, r
(usually written as the Greek letter rho) is the density in kg/m^3, and h is
the height in m (meters).
For example, atmospheric pressure (about 1E5 N/m^2 = 100000 Newtons per
square meter) is sufficient to support about 75 cm (0.75 m) or mercury
(density 13,600 kg/m^3). Plugging in,
p = rgh = 13600 kg/m^3 9.8 m/s^2 0.75
m = 1E5 N/m^2. Check!
In your example, to get water to rise 2 feet (0.6 m), the pressure needed is
p = rgh = 1E3 kg/m^3 9.8 m/s^2 0.6 m = 5.9E3 N/m^2 = 0.84 lb/in^2. This is
suspicious since to generate that pressure with a force of 170 lb, you would
have to spread the force over about 200 in^2, or an area 10 in by 20 in. I
suspect the bottle is supporting most of your weight. In my case, stepping
on the bottom 3 inches of a standard water bottle, the water instantly jumped
well over my head. Note that if I pushed on the water over an area of 3 in
by 3 in (9 in^2) with my 200 lb weight, the pressure would be p = F/A = 200
lb/9 in^2 = 22 lb/in^2 = 1.5E5 N/m^2. This should lift the water to a
height of h = p/(rg) = 15.8 m = 52 ft.
Yes, it is possible to get the water to rise over your head using your body
weight!
Best, Dick Plano, Professor of Physics emeritus, Rutgers University
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Update: June 2012
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