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Show that the total force on a rectangular dam due to the water behind it increases with the square of the water depth. In particular, show that this force is given by $F=\rho g h^{2} L / 2$ , where $\rho$ is the density of water, $h$ is its depth at the dam, and $L$ is the length of the dam. You may assume the face of the dam is vertical. (Hint: Calculate the average pressure exerted and multiply this by the area in contact with the water.

$F_{\text {water }} \propto h^{2}$ and $F_{\text {water }}=\frac{\rho g h^{2} L}{2}$

Physics 101 Mechanics

Chapter 11

Fluid Statics

Fluid Mechanics

University of Michigan - Ann Arbor

Simon Fraser University

Hope College

McMaster University

Lectures

03:45

In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids.

09:49

A fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases and plasmas. Fluids display properties such as flow, pressure, and tension, which can be described with a fluid model. For example, liquids form a surface which exerts a force on other objects in contact with it, and is the basis for the forces of capillarity and cohesion. Fluids are a continuum (or "continuous" in some sense) which means that they cannot be strictly separated into separate pieces. However, there are theoretical limits to the divisibility of fluids. Fluids are in contrast to solids, which are able to sustain a shear stress with no tendency to continue deforming.

02:16

Show that the total force …

07:58

Show that if a vertical da…

19:46

A dam has the shape of a r…

05:50

(III) Water stands at a he…

02:39

For the dam shown, what is…

we're asked to show that the total force on a rectangular damp in the water behind it increases with square of the depth. So we have a picture of our damn here and then we have water on the one side and the pressure, if remember, from how pressure varies with the depth of water, very is linen varies linearly. So it zero up at the surface and then its maximum at bottom. We're told that the height here is ape and the damn has with in three dimensions off l. So the force, by definition, is the pressure is the integral of pressure over area. So if the pressure were constant, then that's just p times a But in this case are pressure is a function of why so we need to actually do the integral. So their area is the x o d Y X goes from zero toe l so actually running in the end of the page and eight and why goes from zero to minus h. We're assuming why is positive up. So this is why minus age now we can right out you are integral out. So we get our pressure as a function of why his row g times. Why now we can pull some things out. Row G is a constant. We do the inner grow from zero toe l over X. Nothing in here depends on act. So we just get an l out, which is constant. So then we have to do the Negro of Why d why? From zero to minus age. And that just gives us each squared over two, giving us the formula that we were given as row G l h squared over two.

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