As the reservoir behind a dam is filled with water, the pressurethat the water exerts on the dam increases. Eventually, the forceon the dam becomes substantial, and it could cause the dam tocollapse. There are two significant issues to be considered: First,the base of the dam should be able to withstand the pressure ,where is the density of the water behind the dam, is its depth, andis the magnitude of the acceleration due to gravity. This meansthat the material of which the dam is made needs to be strongenough so that it doesn't crack (compressive strength).
The second issue has to do with the strength of the foundation ofthe dam. The water pressure exerts a clockwise torque on the dam,as shown in the figure. The foundation of the dam should be strongenough so that the dam does not topple. The material has to bestrong enough that the dam does not snap (shear strength).
To study this phenomenon, consider the simple model of a damdepicted in the diagram. A reservoir of water (density ) behind thedam is filled to a height . Assume that the width of the dam (thedimension pointing into the screen) is .
As the reservoir behind a dam is filled with water, the pressurethat the water exerts on the dam increases. Eventually, the forceon the dam becomes substantial, and it could cause the dam tocollapse. There are two significant issues to be considered: First,the base of the dam should be able to withstand the pressure ,where is the density of the water behind the dam, is its depth, andis the magnitude of the acceleration due to gravity. This meansthat the material of which the dam is made needs to be strongenough so that it doesn't crack (compressive strength).
The second issue has to do with the strength of the foundation ofthe dam. The water pressure exerts a clockwise torque on the dam,as shown in the figure. The foundation of the dam should be strongenough so that the dam does not topple. The material has to bestrong enough that the dam does not snap (shear strength).
To study this phenomenon, consider the simple model of a damdepicted in the diagram. A reservoir of water (density ) behind thedam is filled to a height . Assume that the width of the dam (thedimension pointing into the screen) is .
