In this lesson we are going to learn about an important application of integration. We are going to use integration to calculate the force due to hydrostatic pressure. The idea there is that we have some kind of think plate submerged in a liquid. We are trying to calculate how much force the fluid puts on that thin plate. The key point here is that the fluid does not put so much force on it, but when it is deeper down, there is more fluid piling up and pushing against that plate and so there will be a greater force. We are going to calculate this using certain integral formula.
the units used in the problem carefully. Most commonly, metric units
are used for all quantities in the problem, and your answer will be
in terms of Newtons, i.e. kg m/s² . Less often, English
units will be used and your answer will be in terms of pounds, lb.
Either way, the units should multiply and divide just as numbers do,
which partially checks that you are doing the arithmetic correctly.
are usually fairly complicated word problems. Always read the
problem carefully and start by drawing a picture of the surface.
the depth function D(y) is given by y, y +
c, y − c, or c − y where c is some
constant. Which one it is depends on how you orient your coordinates
in the picture.
limits a and b correspond to the highest and lowest
levels. Again, this depends on how you orient your coordinates in
its feasible, check that your answer makes sense. The amount of
force due to hydrostatic pressure should always be positive!
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.