10. Force Due to Liquid Pressure
by M. Bourne
The force F on an area A at a depth y in a liquid of density w is given by
`F = wyA`
The force will increase if the density increases, or if the depth increases or if the area increases.
So if we have an unevenly shaped plate submerged vertically in a liquid, the force on it will increase with depth. Also, if the shape of the plate changes as we go deeper, we have to allow for this.
So we have:
Now, the total force on the plate is given by
`F=wint_a^bxy\ dy`
where
x is the length (in m) of the element of area (expressed in terms of y)
y is the depth (in m) of the element of area
w is the density of the liquid (in N m-3)
(for water, this is w = 9800 N m-3)
a is the depth at the top of the area in question (in m)
b is the depth at the bottom of the area in question (in m)
Example 1
Find the force on one side of a cubical container `6.0` cm on an edge if the container is filled with mercury. The weight density of mercury is `133` kN/m3.
Example 2
A right triangular plate of base `2.0` m and height `1.0` m is submerged vertically in water, with the top vertex `3.0` m below the surface.
Find the force on one side of the plate.
Didn't find what you are looking for on this page? Try search:
Online Algebra Solver
This algebra solver can solve a wide range of math problems. (Please be patient while it loads.)
Go to: Online algebra solver
Ready for a break?
Play a math game.
(Well, not really a math game, but each game was made using math...)
The IntMath Newsletter
Sign up for the free IntMath Newsletter. Get math study tips, information, news and updates each fortnight. Join thousands of satisfied students, teachers and parents!
Share IntMath!
Short URL for this Page
Save typing! You can use this URL to reach this page:
intmath.com/foliq
Calculus Lessons on DVD
Easy to understand calculus lessons on DVD. See samples before you commit.
More info: Calculus videos
